Samacheer Kalvi solutions for Mathematics - Volume 1 and 2 [English] Class 11 TN Board chapter 11 - Integral Calculus [Latest edition]

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:

e^x

Integrate the following with respect to x:

(1 + x²)^–1 

Integrate the following with respect to x:

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

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)`

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)`

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?

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))`

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"))`

Integrate the following with respect to x:

9xe^3x

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:

27x²e^3x

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:

x⁵e^x2

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))`

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`

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`

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)`

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)`

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)`

Choose the correct alternative:

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

Choose the correct alternative:

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

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

Choose the correct alternative:

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

Choose the correct alternative:

`int sqrt(tanx)/(sin2x)  "d"x` is

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

`int secx/sqrt(cos2x)  "d"x` is

Choose the correct alternative:

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

Choose the correct alternative:

`int 2^(3x + 5)  "d"x` is

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

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

Choose the correct alternative:

`int x^2 cos x  "d"x` is

Choose the correct alternative:

`int sqrt((1 - x)/(1 + x))  "d"x` is

Choose the correct alternative:

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

Choose the correct alternative:

`int "e"^(- 4x) cos   "d"x` is

Choose the correct alternative:

`int (sec^2x)/(tan^2 x - 1)  "d"x`

Choose the correct alternative:

`int "e"^(- 7x) sin 5x  "d"x` is

Choose the correct alternative:

`int x^2 "e"^(x/2)  "d"x` is

Choose the correct alternative:

`int (x + 2)/sqrt(x^2 - 1)  "d"x` is

Choose the correct alternative:

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

Choose the correct alternative:

`int sin sqrt(x)  "d"x` is

Choose the correct alternative:

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