Tamil Nadu Board of Secondary EducationHSC Science Class 11th
Advertisement Remove all ads

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 11 - Integral Calculus [Latest edition]

Chapters

Class 11th Mathematics Volume 1 and 2 Answers Guide - Shaalaa.com
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Chapter 11: Integral Calculus

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.Exercise 11.4Exercise 11.5Exercise 11.6Exercise 11.7Exercise 11.8Exercise 11.9Exercise 11.10Exercise 11.11Exercise 11.12Exercise 11.13
Advertisement Remove all ads
Exercise 11.1 [Page 188]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.1 [Page 188]

Exercise 11.1 | Q 1. (i) | Page 188

Integrate the following with respect to x:

x11 

Exercise 11.1 | Q 1. (ii) | Page 188

Integrate the following with respect to x:

`1/x^7`

Exercise 11.1 | Q 1. (iii) | Page 188

Integrate the following with respect to x:

`root(3)(x^4)`

Exercise 11.1 | Q 1. (iv) | Page 188

Integrate the following with respect to x:

`(x^5)^(1/8)`

Exercise 11.1 | Q 2. (i) | Page 188

Integrate the following with respect to x:

`1/(sin^2x)`

Exercise 11.1 | Q 2. (ii) | Page 188

Integrate the following with respect to x:

`tanx/cosx`

Exercise 11.1 | Q 2. (iii) | Page 188

Integrate the following with respect to x:

`cosx/(sin^2x)`

Exercise 11.1 | Q 2. (iv) | Page 188

Integrate the following with respect to x:

`1/(cos^2x)`

Exercise 11.1 | Q 3. (i) | Page 188

Integrate the following with respect to x:

123 

Exercise 11.1 | Q 3. (ii) | Page 188

Integrate the following with respect to x:

`(x^24)/(x^25)`

Exercise 11.1 | Q 3. (iii) | Page 188

Integrate the following with respect to x:

ex

Exercise 11.1 | Q 4. (i) | Page 188

Integrate the following with respect to x:

(1 + x2)–1 

Exercise 11.1 | Q 4. (ii) | Page 188

Integrate the following with respect to x:

`(1 - x^2)^(- 1/2)`

Exercise 11.2 [Page 190]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.2 [Page 190]

Exercise 11.2 | Q 1. (i) | Page 190

Integrate the following functions with respect to x:

(x + 5)6 

Exercise 11.2 | Q 1. (ii) | Page 190

Integrate the following functions with respect to x:

`1/(2 - 3x)^4`

Exercise 11.2 | Q 1. (iii) | Page 190

Integrate the following functions with respect to x:

`sqrt(3x + 2)`

Exercise 11.2 | Q 2. (i) | Page 190

Integrate the following functions with respect to x:

sin 3x

Exercise 11.2 | Q 2. (ii) | Page 190

Integrate the following functions with respect to x:

cos(5 – 11x)

Exercise 11.2 | Q 2. (iii) | Page 190

Integrate the following functions with respect to x:

cosec2 (5x – 7)

Exercise 11.2 | Q 3. (i) | Page 190

Integrate the following functions with respect to x:

`"e"^(3x - 6)`

Exercise 11.2 | Q 3. (ii) | Page 190

Integrate the following functions with respect to x:

`"e"^(8 - 7x)`

Exercise 11.2 | Q 3. (iii) | Page 190

Integrate the following functions with respect to x:

`1/(6 - 4x)`

Exercise 11.2 | Q 4. (i) | Page 190

Integrate the following functions with respect to x:

`sec^2  x/5`

Exercise 11.2 | Q 4. (ii) | Page 190

Integrate the following functions with respect to x:

cosec(5x + 3) cot(5x + 3)

Exercise 11.2 | Q 4. (iii) | Page 190

Integrate the following functions with respect to x:

30 sec(2 – 15x) tan(2 – 15x)

Exercise 11.2 | Q 5. (i) | Page 190

Integrate the following functions with respect to x:

`1/sqrt(1 - (4x)^2`

Exercise 11.2 | Q 5. (ii) | Page 190

Integrate the following functions with respect to x:

`1/sqrt(1 - 81x^2)`

Exercise 11.2 | Q 5. (iii) | Page 190

Integrate the following functions with respect to x:

`1/sqrt(1 + 36x^2)`

Exercise 11.3, Exercise 11. [Page 192]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.3, Exercise 11. [Page 192]

Exercise 11.3 | Q 1 | Page 192

Integrate the following with respect to x:

`(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)`

Exercise 11.3 | Q 2 | Page 192

Integrate the following with respect to x:

`4 cos(5 - 2x) + 9"e"^(3x  - 6) + 24/(6 - 4x)`

Exercise 11.3 | Q 3 | Page 192

Integrate the following with respect to x:

`sec^2  x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)`

Exercise 11.3 | Q 4 | Page 192

Integrate the following with respect to x:

`8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)`

Exercise 11.3 | Q 5 | Page 192

Integrate the following with respect to x:

`6/(1 + (3x + 2)^2) - 12/sqrt(1 - (3 - 4x)^2`

Exercise 11. | Q 6 | Page 192

Integrate the following with respect to x:

`1/3 cos(x/3 - 4) + 7/(7x + 9) + "e"^(x/5 + 3)`

Exercise 11.4 [Pages 195 - 196]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.4 [Pages 195 - 196]

Exercise 11.4 | Q 1 | Page 195

If f'(x) = 4x – 5 and f(2) = 1, find f(x)

Exercise 11.4 | Q 2 | Page 195

If f'(x) = 9x2 – 6x and f(0) = – 3 find f(x)

Exercise 11.4 | Q 3 | Page 195

If f” (x) = 12x – 6 and f(1) = 30, f’(1) = 5, find f(x)

Exercise 11.4 | Q 4. (i) | Page 196

A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find how long will it take for the ball to strike the ground?

Exercise 11.4 | Q 4. (ii) | Page 196

A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find the speed with which will it strike the ground?

Exercise 11.4 | Q 4. (iii) | Page 196

A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find how high the ball will rise?

Exercise 11.4 | Q 5. (i) | Page 196

A wound is healing in such a way that t days since Sunday the area of the wound has been decreasing at a rate of `- 6/("t" + 2)^2` cm2 per day where 0 < t ≤ 8. If on Monday the area of the wound was 1.4 cm2. What was the area of the wound on Sunday?

Exercise 11.4 | Q 5. (ii) | Page 196

A wound is healing in such a way that t days since Sunday the area of the wound has been decreasing at a rate of `-6/("t" + 2)^2` cm2 per day where 0 < t ≤ 8. If on Monday the area of the wound was 1.4 cm2. What is the anticipated area of the wound on Thursday if it continues to heal at the same rate?

Exercise 11.5 [Page 202]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.5 [Page 202]

Exercise 11.5 | Q 1 | Page 202

Integrate the following functions with respect to x :

`(x^3 + 4x^2 - 3x + 2)/x^2`

Exercise 11.5 | Q 2 | Page 202

Integrate the following functions with respect to x :

`[sqrt(x) + 1/sqrt(x)]^2`

Exercise 11.5 | Q 3 | Page 202

Integrate the following functions with respect to x :

(2x – 5)(3x + 4x)

Exercise 11.5 | Q 4 | Page 202

Integrate the following functions with respect to x :

cot2x + tan2x

Exercise 11.5 | Q 5 | Page 202

Integrate the following functions with respect to x :

`(cos2x - cos 2 alpha)/(cosx - cos alpha)`

Exercise 11.5 | Q 6 | Page 202

Integrate the following functions with respect to x :

`(cos 2x)/(sin^2x cos^2x)`

Exercise 11.5 | Q 7 | Page 202

Integrate the following functions with respect to x :

`(3 + 4cosx)/(sin^2x)`

Exercise 11.5 | Q 8 | Page 202

Integrate the following functions with respect to x :

`(sin^2x)/(1 + cosx)`

Exercise 11.5 | Q 9 | Page 202

Integrate the following functions with respect to x :

`(sin4x)/sinx`

Exercise 11.5 | Q 10 | Page 202

Integrate the following functions with respect to x :

cos 3x cos 2x

Exercise 11.5 | Q 11 | Page 202

Integrate the following functions with respect to x :

sin2 5x

Exercise 11.5 | Q 12 | Page 202

Integrate the following functions with respect to x :

`(1 + cos 4x)/(cos x - tan x)`

Exercise 11.5 | Q 13 | Page 202

Integrate the following functions with respect to x :

`"e"^(x log "a") "e"^x`

Exercise 11.5 | Q 14 | Page 202

Integrate the following functions with respect to x :

`(3x + 4) sqrt(3x + 7)`

Exercise 11.5 | Q 15 | Page 202

Integrate the following functions with respect to x :

`(8^(1 + x) + 4^(1 - x))/2^x`

Exercise 11.5 | Q 16 | Page 202

Integrate the following functions with respect to x :

`1/(sqrt(x + 3) - sqrt(x - 4))`

Exercise 11.5 | Q 17 | Page 202

Integrate the following functions with respect to x :

`(x + 1)/((x + 2)(x + 3))`

Exercise 11.5 | Q 18 | Page 202

Integrate the following functions with respect to x :

`1/((x - 1)(x + 2)^2`

Exercise 11.5 | Q 19 | Page 202

Integrate the following functions with respect to x :

`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`

Exercise 11.5 | Q 20 | Page 202

Integrate the following functions with respect to x :

`x^3/((x - 1)(x - 2))`

Exercise 11.6 [Page 206]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.6 [Page 206]

Exercise 11.6 | Q 1 | Page 206

Integrate the following with respect to x :

`x/sqrt(1 + x^2)`

Exercise 11.6 | Q 2 | Page 206

Integrate the following with respect to x :

`x^2/(1 + x^6)`

Exercise 11.6 | Q 3 | Page 206

Integrate the following with respect to x :

`("e"^x - "e"^-x)/("e"^x + "e"^-x)`

Exercise 11.6 | Q 4 | Page 206

Integrate the following with respect to x :

`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`

Exercise 11.6 | Q 5 | Page 206

Integrate the following with respect to x :

`(sin sqrt(x))/sqrt(x)`

Exercise 11.6 | Q 6 | Page 206

Integrate the following with respect to x :

`cot x/(log(sin x))`

Exercise 11.6 | Q 7 | Page 206

Integrate the following with respect to x :

`("cosec"  x)/(log(tan  x/2))`

Exercise 11.6 | Q 8 | Page 206

Integrate the following with respect to x :

`(sin 2x)/("a"^2 + "b"^2 sin^2x)`

Exercise 11.6 | Q 9 | Page 206

Integrate the following with respect to x :

`(sin^-1 x)/sqrt(1 - x^2)`

Exercise 11.6 | Q 10 | Page 206

Integrate the following with respect to x :

`sqrt(x)/(1 + sqrt(x))`

Exercise 11.6 | Q 11 | Page 206

Integrate the following with respect to x :

`1/(x log x log (log x))`

Exercise 11.6 | Q 12 | Page 206

Integrate the following with respect to x :

`alpha beta  x^(alpha - 1)  "e"^(- beta x^alpha)`

Exercise 11.6 | Q 13 | Page 206

Integrate the following with respect to x :

`tan x sqrt(sec x)`

Exercise 11.6 | Q 14 | Page 206

Integrate the following with respect to x :

x(1 – x)17

Exercise 11.6 | Q 15 | Page 206

Integrate the following with respect to x :

sin5x cos3x

Exercise 11.6 | Q 16 | Page 206

Integrate the following with respect to x :

`cosx/(cos(x - "a"))`

Exercise 11.7 [Page 210]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.7 [Page 210]

Exercise 11.7 | Q 1. (i) | Page 210

Integrate the following with respect to x:

9xe3x

Exercise 11.7 | Q 1. (i) | Page 210

Integrate the following with respect to x:

x sin 3x

Exercise 11.7 | Q 1. (iii) | Page 210

Integrate the following with respect to x:

25xe–5x 

Exercise 11.7 | Q 1. (iv) | Page 210

Integrate the following with respect to x:

x sec x tan x

Exercise 11.7 | Q 2. (i) | Page 210

Integrate the following with respect to x:

x log x

Exercise 11.7 | Q 2. (ii) | Page 210

Integrate the following with respect to x:

27x2e3x

Exercise 11.7 | Q 2. (iii) | Page 210

Integrate the following with respect to x:

x2 cos x

Exercise 11.7 | Q 2. (iv) | Page 210

Integrate the following with respect to x:

x3 sin x

Exercise 11.7 | Q 3. (i) | Page 210

Integrate the following with respect to x:

`(x sin^-1 x)/sqrt(1 - x^2)`

Exercise 11.7 | Q 3. (ii) | Page 210

Integrate the following with respect to x:

x5ex2

Exercise 11.7 | Q 3. (iii) | Page 210

Integrate the following with respect to x:

`tan^-1 ((8x)/(1 - 16x^2))`

Exercise 11.7 | Q 3. (iv) | Page 210

Integrate the following with respect to x:

`sin^-1 ((2x)/(1 + x^2))`

Exercise 11.8 [Page 212]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.8 [Page 212]

Exercise 11.8 | Q 1. (i) | Page 212

Integrate the following with respect to x:

`"e"^("a"x) cos"b"x`

Exercise 11.8 | Q 1. (ii) | Page 212

Integrate the following with respect to x:

`"e"^(2x) sinx`

Exercise 11.8 | Q 1. (iii) | Page 212

Integrate the following with respect to x:

`"e"^(-x) cos 2x`

Exercise 11.8 | Q 2. (i) | Page 212

Integrate the following with respect to x:

`"e"^(- 3x) sin 2x`

Exercise 11.8 | Q 2. (ii) | Page 212

Integrate the following with respect to x:

`"e"^(- 4x) sin 2x`

Exercise 11.8 | Q 2. (iii) | Page 212

Integrate the following with respect to x:

`"e"^(- 3x) cos x`

Exercise 11.9 [Page 213]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.9 [Page 213]

Exercise 11.9 | Q 1 | Page 213

Integrate the following with respect to x:

`"e"^x (tan x + log sec x)`

Exercise 11.9 | Q 2 | Page 213

Integrate the following with respect to x:

`"e"^x ((x - 1)/(2x^2))`

Exercise 11.9 | Q 3 | Page 213

Integrate the following with respect to x:

`"e"^x sec x(1 + tan x)`

Exercise 11.9 | Q 4 | Page 213

Integrate the following with respect to x:

`"e"^x ((2 + sin 2x)/(1 + cos 2x))`

Exercise 11.9 | Q 5 | Page 213

Integrate the following with respect to x:

`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`

Exercise 11.9 | Q 6 | Page 213

Integrate the following with respect to x:\

`logx/(1 + log)^2`

Exercise 11.10 [Page 219]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.10 [Page 219]

Exercise 11.10 | Q 1. (i) | Page 219

Find the integrals of the following:

`1/(4 - x^2)`

Exercise 11.10 | Q 1. (ii) | Page 219

Find the integrals of the following:

`1/(25 - 4x^2)`

Exercise 11.10 | Q 1. (iii) | Page 219

Find the integrals of the following:

`1/(9x^2 - 4)`

Exercise 11.10 | Q 2. (i) | Page 219

Find the integrals of the following:

`1/(6x - 7 - x^2)`

Exercise 11.10 | Q 2. (ii) | Page 219

Find the integrals of the following:

`1/((x + 1)^2 - 25)`

Exercise 11.10 | Q 2. (iii) | Page 219

Find the integrals of the following:

`1/sqrt(xx^2 + 4x + 2)`

Exercise 11.10 | Q 3. (i) | Page 219

Find the integrals of the following:

`1/sqrt((2 + x)^2 - 1)`

Exercise 11.10 | Q 3. (ii) | Page 219

Find the integrals of the following:

`1/sqrt(x^2 - 4x + 5)`

Exercise 11.10 | Q 3. (iii) | Page 219

Find the integrals of the following:

`1/sqrt(9 + 8x - x^2)`

Exercise 11.11 [Page 222]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.11 [Page 222]

Exercise 11.11 | Q 1. (i) | Page 222

Integrate the following with respect to x:

`(2x - 3)/(x^2 + 4x - 12)`

Exercise 11.11 | Q 1. (ii) | Page 222

Integrate the following with respect to x:

`(5x - 2)/(2 + 2x + x^2)`

Exercise 11.11 | Q 1. (iii) | Page 222

Integrate the following with respect to x:

`(3x + 1)/(2x^2 - 2x + 3)`

Exercise 11.11 | Q 2. (i) | Page 222

Integrate the following with respect to x:

`(2x + 1)/sqrt(9 + 4x - x^2)`

Exercise 11.11 | Q 2. (ii) | Page 222

Integrate the following with respect to x:

`(x + 2)/sqrt(x^2 - 1)`

Exercise 11.11 | Q 2. (iii) | Page 222

Integrate the following with respect to x:

`(2x + 3)/sqrt(x^2 + 4x + 1)`

Exercise 11.12 [Page 225]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.12 [Page 225]

Exercise 11.12 | Q 1. (i) | Page 225

Integrate the following functions with respect to x:

`sqrt(x^2 + 2x + 10)`

Exercise 11.12 | Q 1. (ii) | Page 225

Integrate the following functions with respect to x:

`sqrt(x^2 - 2x - 3)`

Exercise 11.12 | Q 1. (iii) | Page 225

Integrate the following functions with respect to x:

`sqrt((6 - x)(x - 4))`

Exercise 11.12 | Q 2. (i) | Page 225

Integrate the following functions with respect to x:

`sqrt(9 - (2x + 5)^2`

Exercise 11.12 | Q 2. (ii) | Page 225

Integrate the following functions with respect to x:

`sqrt(81 + (2x + 1)^2`

Exercise 11.12 | Q 2. (iii) | Page 225

Integrate the following functions with respect to x:

`sqrt((x + 1)^2 - 4)`

Exercise 11.13 [Pages 225 - 227]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral CalculusExercise 11.13 [Pages 225 - 227]

Exercise 11.13 | Q 1 | Page 225

Choose the correct alternative:

If `int f(x) "d"x = g(x) + "c",` then `int f(x)g"'"(x) "d"x`

  • `int (f(x))^2 "d"x`

  • `int f(x) g(x) "d"x`

  • `int f"'"(x)g(x)  "d"x`

  • `int (g(x))^2  "d"x`

Exercise 11.13 | Q 2 | Page 225

Choose the correct alternative:

If `int 3^(1/x)/x^2  "d"x = "k"(3^(1/x)) + "c"`, then the value of k is

  • log 3

  • – log 3

  • `- 1/log 3`

  • `1/log 3`

Exercise 11.13 | Q 3 | Page 225

Choose the correct alternative:

If `int f"'"(x)"e"^(x^2) "d"x = (x - 1)"e"^(x^2) + "c"`, then`f(x)` is

  • `2x^3 - x^2/2 + x + "c"`

  • `x^3/2 + 3x^2 + 4x + "c"`

  • `x^3 + 4x^2 + 6x + "c"`

  • `(2x^3)/3 - x^2 + x + "c"`

Exercise 11.13 | Q 4 | Page 225

Choose the correct alternative:

The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is

  • y = `x + 4/x + 3`

  • y = `x + 4/x + 4`

  • y = x2 + 3x + 4

  • y = x2 – 3x + 6

Exercise 11.13 | Q 5 | Page 225

Choose the correct alternative:

`int ("e"^x (1 + x))/(cos^2(x"e"^x))  "d"x` is

  • `cot(x"e"^x) + "c"`

  • `sec(x"e"^x) + "c"`

  • `tan(x"e"^x) + "c"`

  • `cos(x"e"^x) + "c"`

Exercise 11.13 | Q 6 | Page 225

Choose the correct alternative:

`int sqrt(tanx)/(sin2x)  "d"x` is

  • `sqrt(tan x) + "c"`

  • `2sqrt(tan x) + "c"`

  • `1/2 sqrt(tan x) + "c"`

  • `1/4 sqrt(tan x) + "c"`

Exercise 11.13 | Q 7 | Page 225

Choose the correct alternative:

`int sin^2x "d"x` is

  • `(- 3)/4 cos x - (cos3x)/12 + "c"`

  • `3/4 cos x + (cos3x)/12 + "c"`

  • `(- 3)/4 cos x + (cos3x)/12 + "c"`

  • `(- 3)/4 sin x - (sin3x)/12 + "c"`

Exercise 11.13 | Q 8 | Page 225

Choose the correct alternative:

`int ("e"^(6 log x) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx))  "d"x` is

  • x + c

  • `x^3/3 + "c"`

  • `3/x^3 + "c"`

  • `1/x^2 + "c"`

Exercise 11.13 | Q 9 | Page 226

Choose the correct alternative:

`int secx/sqrt(cos2x)  "d"x` is

  • `tan^-1 (sin x) + "c"`

  • `2sin^-1 (tan x) + "c"`

  • `tan^-1 (cos x) + "c"`

  • `sin^-1 (tan x) + "c"`

Exercise 11.13 | Q 10 | Page 226

Choose the correct alternative:

`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x))  "d"x` is

  • x2 + c

  • 2x2 + c

  • `x^2/2 + "c"`

  • `- x^2/2 + "c"`

Exercise 11.13 | Q 11 | Page 226

Choose the correct alternative:

`int 2^(3x + 5)  "d"x` is

  • `(3(2^(3x + 5)))/log2 + "c"`

  • `2^(3x + 5)/(2log(3x + 5)) + "c"`

  • `2^(3x + 5)/(2log3) + "c"`

  • `2^(3x + 5)/(3log2) + "c"`

Exercise 11.13 | Q 12 | Page 226

Choose the correct alternative:

`int (sin^2x - cos^8x)/(1 - 2sin^x cosx)  "d"x` is

  • `1/2 sin 2x + "c"`

  • `- 1/2 sin 2x + "c"`

  • `1/2 cos 2x + "c"`

  • `- 1/2 cos 2x + "c"`

Exercise 11.13 | Q 13 | Page 226

Choose the correct alternative:

`int ("e"^x(x^2 tan^-1x + tan^-1x + 1))/(x^2 + 1)  "d"x` is

  • ex tan-1 (x + 1) + c

  • tan-1 (ex) + c

  • `"e"^x (tan^-1 x)^2/2 + "c"`

  • ex tan-1 x + c

Exercise 11.13 | Q 14 | Page 226

Choose the correct alternative:

`int (x^2 + cos^2x)/(x^2 + 1)  "cosec"^2 x/("d"x)` is

  • cot x + sin-1 x + c

  • – cot x + tan-1x + c

  • – tan x + cot-1 x + c

  • – cot x – tan-1x + c

Exercise 11.13 | Q 15 | Page 226

Choose the correct alternative:

`int x^2 cos x  "d"x` is

  • x2 sin x + 2x cos x – 2 sin x + c

  • x2 sin x – 2x cos x – 2 sin x + c

  • – x2 sin x + 2x cos x + 2 sin x + c

  • – x2 sin x – 2x cos x + 2 sin x + c

Exercise 11.13 | Q 16 | Page 226

Choose the correct alternative:

`int sqrt((1 - x)/(1 + x))  "d"x` is

  • `sqrt(1 - x^2) + sin^-1x + "c"`

  • `sin^-1x - sqrt(1 - x^2) + "c"`

  • `log |x + sqrt(1 - x^2)| - sqrt(1 - x^2) + "c"`

  • `sqrt(1 - x^2) + log|x + sqrt(1 - x^2)| + "c"`

Exercise 11.13 | Q 17 | Page 226

Choose the correct alternative:

`int ("d"x)/("e"^x - 1)` is

  • `log |"e"^x| - log|"e"^x - 1| + "c"`

  • `log |"e"^x| + log|"e"^x - 1| + "c"`

  • `log |"e"^x - 1| - log|"e"^x| + "c"`

  • `log |"e"^x + 1| - log|"e"^x| + "c"`

Exercise 11.13 | Q 18 | Page 227

Choose the correct alternative:

`int "e"^(- 4x) cos   "d"x` is

  • `"e"^(- 4x)/17  [4cos x - sin x] + "c"`

  • `"e"^(- 4x)/17  [- 4cos x + sin x] + "c"`

  • `"e"^(- 4x)/17  [4cos x + sin x] + "c"`

  • `"e"^(- 4x)/17  [- 4cos x - sin x] + "c"`

Exercise 11.13 | Q 19 | Page 227

Choose the correct alternative:

`int (sec^2x)/(tan^2 x - 1)  "d"x`

  • `2 log |(1 - tan x)/(1 + tan x)| + "c"`

  • `log |(1 + tan x)/(1 - tan x)| + "c"`

  • `1/2 log |(tan x + 1)/(tan x - 1)| + "c"`

  • `1/2 log |(tan x - 1)/(tan x + 1)| + "c"`

Exercise 11.13 | Q 20 | Page 227

Choose the correct alternative:

`int "e"^(- 7x) sin 5x  "d"x` is

  • `"e"^(- 7x)/74  [- 7 sin 5x - 5 cos 5x] + "c"`

  • `"e"^(- 7x)/74  [7 sin 5x + 5 cos 5x] + "c"`

  • `"e"^(- 7x)/74  [7 sin 5x - 5 cos 5x] + "c"`

  • `"e"^(- 7x)/74  [- 7 sin 5x + 5 cos 5x] + "c"`

Exercise 11.13 | Q 21 | Page 227

Choose the correct alternative:

`int x^2 "e"^(x/2)  "d"x` is

  • `x^2 "e"^(x/2) - 4x"e"^(x/2) - 8"e"^(x/2) + "c"`

  • `2x^2 "e"^(x/2) - 8x"e"^(x/2) - 16"e"^(x/2) + "c"`

  • `2x^2 "e"^(x/2) - 8x"e"^(x/2) + 16"e"^(x/2) + "c"`

  • `x^2 "e"^(x/2)/2 - (x"e"^(x/2))/4 + "e"^(x/2)/8 + "c"`

Exercise 11.13 | Q 22 | Page 227

Choose the correct alternative:

`int (x + 2)/sqrt(x^2 - 1)  "d"x` is

  • `sqrt(x^2  - 1) - 2log |x + sqrt(x^2 - 1)| + "c"`

  • `sin^-1x - 2log |x + sqrt(x^2 - 1)| + "c"`

  • `2log |x + sqrt(x^2 - 1)| - sin^-1x + "c"`

  • `sqrt(x^2  - 1) + 2log |x + sqrt(x^2 - 1)| + "c"`

Exercise 11.13 | Q 23 | Page 227

Choose the correct alternative:

`int 1/(x sqrt(log x)^2 - 5)  "d"x` is

  • `log |x + sqrt(x^2 - 5)| + "c"`

  • `log|log x + sqrt(log x - 5)| + "c"`

  • `log|log x + sqrt((log x)^2 - 5)| + "c"`

  • `log|log x - sqrt((log x)^2 - 5)| + "c"`

Exercise 11.13 | Q 24 | Page 227

Choose the correct alternative:

`int sin sqrt(x)  "d"x` is

  • `2(- sqrt(x) cos sqrt(x) + sin sqrt(x)) + "c"`

  • `2(- sqrt(x) cos sqrt(x) - sin sqrt(x)) + "c"`

  • `2(- sqrt(x) sin sqrt(x) - cos sqrt(x)) + "c"`

  • `2(- sqrt(x) sin sqrt(x) + cos sqrt(x)) + "c"`

Exercise 11.13 | Q 25 | Page 227

Choose the correct alternative:

`int "e"^(sqrt(x)) "d"x` is

  • `2sqrt(x) (1 - "e"^(sqrt(x))) + "c"`

  • `2sqrt(x) ("e"^(sqrt(x)) - 1) + "c"`

  • `2"e"^(sqrt(x)) (1 - sqrt(x)) + "c"`

  • `2"e"^(sqrt(x)) (sqrt(x) - 1) + "c"`

Chapter 11: Integral Calculus

Exercise 11.1Exercise 11.2Exercise 11.3Exercise 11.Exercise 11.4Exercise 11.5Exercise 11.6Exercise 11.7Exercise 11.8Exercise 11.9Exercise 11.10Exercise 11.11Exercise 11.12Exercise 11.13
Class 11th Mathematics Volume 1 and 2 Answers Guide - Shaalaa.com

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 11 - Integral Calculus

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 11 (Integral Calculus) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 11th Mathematics Volume 1 and 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Tamil Nadu Board Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 11 Integral Calculus are Integral Calculus, Newton-leibnitz Integral, Basic Rules of Integration, Integrals of the Form, Properties of Integrals, Simple Applications, Methods of Integration.

Using Tamil Nadu Board Samacheer Kalvi Class 11th solutions Integral Calculus exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Tamil Nadu Board Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 11th prefer Tamil Nadu Board Samacheer Kalvi Textbook Solutions to score more in exam.

Get the free view of chapter 11 Integral Calculus Class 11th extra questions for Class 11th Mathematics Volume 1 and 2 Answers Guide and can use Shaalaa.com to keep it handy for your exam preparation

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×