Chapters
Chapter 2: Basic Algebra
Chapter 3: Trigonometry
Chapter 4: Combinatorics and Mathematical Induction
Chapter 5: Binomial Theorem, Sequences and Series
Chapter 6: Two Dimensional Analytical Geometry
Chapter 7: Matrices and Determinants
Chapter 8: Vector Algebra
Chapter 9: Differential Calculus - Limits and Continuity
Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation
Chapter 11: Integral Calculus
Chapter 12: Introduction to probability theory
Chapter 11: Integral Calculus
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.1 [Page 188]
Integrate the following with respect to x:
x11
Integrate the following with respect to x:
`1/x^7`
Integrate the following with respect to x:
`root(3)(x^4)`
Integrate the following with respect to x:
`(x^5)^(1/8)`
Integrate the following with respect to x:
`1/(sin^2x)`
Integrate the following with respect to x:
`tanx/cosx`
Integrate the following with respect to x:
`cosx/(sin^2x)`
Integrate the following with respect to x:
`1/(cos^2x)`
Integrate the following with respect to x:
123
Integrate the following with respect to x:
`(x^24)/(x^25)`
Integrate the following with respect to x:
ex
Integrate the following with respect to x:
(1 + x2)–1
Integrate the following with respect to x:
`(1 - x^2)^(- 1/2)`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.2 [Page 190]
Integrate the following functions with respect to x:
(x + 5)6
Integrate the following functions with respect to x:
`1/(2 - 3x)^4`
Integrate the following functions with respect to x:
`sqrt(3x + 2)`
Integrate the following functions with respect to x:
sin 3x
Integrate the following functions with respect to x:
cos(5 – 11x)
Integrate the following functions with respect to x:
cosec2 (5x – 7)
Integrate the following functions with respect to x:
`"e"^(3x - 6)`
Integrate the following functions with respect to x:
`"e"^(8 - 7x)`
Integrate the following functions with respect to x:
`1/(6 - 4x)`
Integrate the following functions with respect to x:
`sec^2 x/5`
Integrate the following functions with respect to x:
cosec(5x + 3) cot(5x + 3)
Integrate the following functions with respect to x:
30 sec(2 – 15x) tan(2 – 15x)
Integrate the following functions with respect to x:
`1/sqrt(1 - (4x)^2`
Integrate the following functions with respect to x:
`1/sqrt(1 - 81x^2)`
Integrate the following functions with respect to x:
`1/sqrt(1 + 36x^2)`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.3 [Page 192]
Integrate the following with respect to x:
`(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)`
Integrate the following with respect to x:
`4 cos(5 - 2x) + 9"e"^(3x - 6) + 24/(6 - 4x)`
Integrate the following with respect to x:
`sec^2 x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)`
Integrate the following with respect to x:
`8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)`
Integrate the following with respect to x:
`6/(1 + (3x + 2)^2) - 12/sqrt(1 - (3 - 4x)^2`
Integrate the following with respect to x:
`1/3 cos(x/3 - 4) + 7/(7x + 9) + "e"^(x/5 + 3)`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.4 [Pages 195 - 196]
If f'(x) = 4x – 5 and f(2) = 1, find f(x)
If f'(x) = 9x2 – 6x and f(0) = – 3 find f(x)
If f” (x) = 12x – 6 and f(1) = 30, f’(1) = 5, find f(x)
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?
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?
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?
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?
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?
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.5 [Page 202]
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
cot2x + tan2x
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
cos 3x cos 2x
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
Integrate the following functions with respect to x :
`(8^(1 + x) + 4^(1 - x))/2^x`
Integrate the following functions with respect to x :
`1/(sqrt(x + 3) - sqrt(x - 4))`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following functions with respect to x :
`(3x - 9)/((x - 1)(x + 2)(x^2 + 1))`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.6 [Page 206]
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`("e"^x - "e"^-x)/("e"^x + "e"^-x)`
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Integrate the following with respect to x :
`(sin sqrt(x))/sqrt(x)`
Integrate the following with respect to x :
`cot x/(log(sin x))`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`sqrt(x)/(1 + sqrt(x))`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`tan x sqrt(sec x)`
Integrate the following with respect to x :
x(1 – x)17
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.7 [Page 210]
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
x sec x tan x
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x2 cos x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.8 [Page 212]
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^(- 3x) sin 2x`
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.9 [Page 213]
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Integrate the following with respect to x:
`"e"^x sec x(1 + tan x)`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Integrate the following with respect to x:
`"e"^(tan^-1 x) ((1 + x + x^2)/(1 + x^2))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.10 [Page 219]
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/(9x^2 - 4)`
Find the integrals of the following:
`1/(6x - 7 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.11 [Page 222]
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.12 [Page 225]
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Integrate the following functions with respect to x:
`sqrt((x + 1)^2 - 4)`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 11 Integral Calculus Exercise 11.13 [Pages 225 - 227]
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`
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`
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"`
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
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"`
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"`
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"`
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"`
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"`
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"`
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"`
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"`
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
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
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
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"`
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"`
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"`
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"`
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"`
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"`
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"`
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"`
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"`
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
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
