Tamil Nadu Board of Secondary EducationHSC Science Class 11th

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

## 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
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", thenf(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

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

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