Class 12 Mathematics - Chapter 7: Integrals MCQ Questions

29 Questions 58 Minutes

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Your Class 12 Mathematics Study Path

Question 1

âˆ«(frac { sin^2 x – cos ^2 x }{sin^2 x cos^2 x}) dx is equals to

A tan x + sec x + c.

B -tan x + cot x + c

C tan x + cosec x + c

D tan x + cot x + c

Question 2

If x = (int_{0}^{y}) (frac { dt }{sqrt{1+9t^2}}) and (frac { d^y }{dx^2}) = ay, then a is equal to

A 1.

B 9

C 6

D 3

Question 3

(int_{1}^{sqrt{3}}) (frac { dx }{1+x^2}) equals

A (frac { Ï€ }{112})

B (frac { Ï€ }{6})

C (frac { 2Ï€ }{3})

D (frac { Ï€ }{3})

Question 4

If (int_{0}^{1}) (frac { e^t }{1+t}) dt = a, then (int_{0}^{1}) (frac { e^t }{(1+t)^2})

A a + 1 + (frac { e }{2})

B a – 1 – (frac { e }{2})

C a + 1 – (frac { e }{2})

D a – 1 + (frac { e }{2})

Question 5

âˆ«(frac { dx }{x^2+2x+2}) equals

A tan^-1 x + c.

B (x + 1) tan^-1 x + c

C tan^-1 (x + 1) + c

D x tan^-1 (x + 1) + c

Question 6

Let I = (int_{0}^{1}) (frac { sin x }{âˆšx}) dx and J = (int_{0}^{1}) (frac { cos x }{âˆšx}) dx. Then which of the following is true?

A I < (frac { 2 }{3}) and J > 2.

B I < (frac { 2 }{3}) and J < 2

C I > (frac { 2 }{3}) and J > 2

D I > (frac { 2 }{3}) and J < 2

Question 7

(int_{-Ï€/2}^{Ï€/2}) (xÂ³ + x cos x + tan⁵ x + 1) dx is

A 1

B Ï€

C 2

Question 8

âˆ«e^x(cos x – sin x)dx is equal to

A -e^x sin x + c.

B -e^x cos x + c

C e^x sin x + c

D e^x – cos x + c

Question 9

âˆ«xÂ² e^xÂ³ dx equals

A (frac { 1 }{2}) e^xÂ² + c

B (frac { 1 }{2}) e^xÂ³ + c

C (frac { 1 }{3}) e^xÂ² + c

D (frac { 1 }{3}) e^xÂ³ + c

Question 10

âˆ«(frac { dx }{x(x^2+1)}) equals

A log |x| + log (xÂ² + 1) + c

B -log |x| + (frac { 1 }{2}) log (xÂ² + 1) + c

C (frac { 1 }{2}) log |x| + (frac { 1 }{2}) log (xÂ² + 1) + c

D log |x| – (frac { 1 }{2}) log (xÂ² + 1) + c

Question 11

(int_{0}^{Ï€}) [cot x]dx, where [ . ] denotes the greatest integer function, is equal to

A –(frac { Ï€ }{2})

B -1

C 2

D (frac { Ï€ }{2})

Question 12

(int_{1}^{2/3}) (frac { dx }{4+9x^2}) equals

A (frac { Ï€ }{4})

B (frac { Ï€ }{24})

C (frac { Ï€ }{12})

D (frac { Ï€ }{6})

Question 13

âˆ«e^x sec x (1 + tan x) dx equals

A e^x tan x + c.

B e^x sin x + c

C e^x sec x + c

D e^x cos x + c

Question 14

âˆ«(frac { dx }{sin^2 x cos^2 x}) is equal to

A (tan x – cot x)Â² + c.

B tan x – cot x + c

C (tan x + cot x)Â² + c

D tan x + cot x + c

Question 15

âˆ«(frac { dx }{sin^2 x cos^2 x}) equals

A tan x – cot 2x + c.

B tan x cot x + c

C tan x – cot x + c

D tan x + cot x + c

Question 16

Then (int_{0}^{1}) p(x) dx equals

A 42

B 41

C 21

D (sqrt { 41})

Question 17

âˆ«(frac { dx }{e^x+e{-x}}) is equal to

A log (e^x + e^-x) + c.

B log (e^x – e^-1) + c

C tan^-1 (e^-x) + c

D tan^-1 (e^x) + c

Question 18

The value of (int_{0}^{Ï€/2}) log ((frac { 4+3 sin x }{4+3 cos x})) dx is

A -2

C (frac { 3 }{4})

D 2

Question 19

If I₄ + I₆ = a tan⁵ x + bx⁵ + c, where c is a constant of integration, then the ordered pair (a, b) is equal to

A ((frac { 1}{5}), 0)

B (-(frac { 1}{5}), 1)

C (-(frac { 1}{5}), 0)

D ((frac { 1}{5}), -1)

Question 20

âˆ«(frac { e^x(1 + x) }{cos^2(xe^2)}) dx is equals to

A cot (e^x) + c

B tan (e^x) + c

C tan (xe^x) + c

D -cot (xe^x) + c

Question 21

âˆ«tan^-1 âˆšx dx is equal to

A ^-1x – (x + 1) tan^-1 âˆšx + c

B âˆšx – x tan^-1 âˆšx + c

C x tan^-1 âˆšx – âˆšx + c

D (x + 1)tan^-1 âˆšx – âˆšx + c

Question 22

(int_{a+c}^{b+c}) f(x)dx is equal to :

A (int_{a-c}^{b-c})

B (int_{c}^{b}) f(x)dx

C (int_{c}^{b}) f(x + c)dx

D (int_{c}^{b}) f(x – c)dx

Question 23

âˆ«(frac { cos 2x }{(sin x + cos x)^2}) dx is equal to

A (frac { 1 }{(sin x + cos x)^2}) + c

B log |sin x – cos x| + c

C log |sin x + cos x| + c

D (frac { -1 }{sin x + cos x}) + c

Question 24

(int_{c}^{b}) |x cos Ï€x|dx is equal to

A (frac { 1 }{Ï€})

B (frac { 2 }{Ï€})

C (frac { 4 }{Ï€})

D (frac { 8 }{Ï€})

Question 25

âˆ«(frac { 10x^9+10^x log_e 10 }{x^{10} + 10^x}) dx equals

A log (10^x + x¹⁰) + c.

B (10^x – x¹⁰)^-1 + c

C 10^x + x¹⁰ + c

D 10^x -x¹⁰ + c

Question 26

If âˆ« (frac { 3e^x-5e^{-x} }{4r^x+5e^{-x}}) dx = ax + b log |4e^x + 5e^-x| + c then

A a = (frac { 1 }{8}), b = –(frac { 7 }{8)

Answer

Answer: a = –(frac { 1 }{8}), b = (frac { 7 }{8})

B a = (frac { -1 }{8}), b = –(frac { 7 }{8})

C a = (frac { 1 }{8}), b = (frac { 7 }{8})

D a = –(frac { 1 }{8}), b = (frac { 7 }{8})

Question 27

(int_{-1}^{1}) (frac { x^3+|x|+1 }{x^2+2|x|+1}) is equal to

A 4 log 2

B (frac { 1 }{2}) log 2

C 2 log 2

D log 2

Question 28

The value of the integral (int_{1}^{2/3}) (frac { (x-x^3)^{1/3} }{x^4}) dx is

A 4

B 3

D 6

Question 29

The value of (int_{-Ï€/2}^{Ï€/2}) (frac { sin^2 x }{1 + 2^x}) dx is

A (frac {Ï€}{4})

B 4Ï€

C (frac {Ï€}{2})

D (frac { Ï€}{8})

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Class 12 Mathematics - Chapter 7: Integrals MCQ Questions

Your Class 12 Mathematics Study Path

âˆ«(frac { sin^2 x – cos ^2 x }{sin^2 x cos^2 x}) dx is equals to

If x = (int_{0}^{y}) (frac { dt }{sqrt{1+9t^2}}) and (frac { d^y }{dx^2}) = ay, then a is equal to

(int_{1}^{sqrt{3}}) (frac { dx }{1+x^2}) equals

If (int_{0}^{1}) (frac { e^t }{1+t}) dt = a, then (int_{0}^{1}) (frac { e^t }{(1+t)^2})

âˆ«(frac { dx }{x^2+2x+2}) equals

Let I = (int_{0}^{1}) (frac { sin x }{âˆšx}) dx and J = (int_{0}^{1}) (frac { cos x }{âˆšx}) dx. Then which of the following is true?

(int_{-Ï€/2}^{Ï€/2}) (xÂ³ + x cos x + tan5 x + 1) dx is

âˆ«ex(cos x – sin x)dx is equal to

âˆ«xÂ² exÂ³ dx equals

âˆ«(frac { dx }{x(x^2+1)}) equals

(int_{0}^{Ï€}) [cot x]dx, where [ . ] denotes the greatest integer function, is equal to

(int_{1}^{2/3}) (frac { dx }{4+9x^2}) equals

âˆ«ex sec x (1 + tan x) dx equals

âˆ«(frac { dx }{sin^2 x cos^2 x}) is equal to

âˆ«(frac { dx }{sin^2 x cos^2 x}) equals

Then (int_{0}^{1}) p(x) dx equals

âˆ«(frac { dx }{e^x+e{-x}}) is equal to

The value of (int_{0}^{Ï€/2}) log ((frac { 4+3 sin x }{4+3 cos x})) dx is

If I4 + I6 = a tan5 x + bx5 + c, where c is a constant of integration, then the ordered pair (a, b) is equal to

âˆ«(frac { e^x(1 + x) }{cos^2(xe^2)}) dx is equals to

âˆ«tan-1 âˆšx dx is equal to

(int_{a+c}^{b+c}) f(x)dx is equal to :

âˆ«(frac { cos 2x }{(sin x + cos x)^2}) dx is equal to

(int_{c}^{b}) |x cos Ï€x|dx is equal to

âˆ«(frac { 10x^9+10^x log_e 10 }{x^{10} + 10^x}) dx equals

If âˆ« (frac { 3e^x-5e^{-x} }{4r^x+5e^{-x}}) dx = ax + b log |4ex + 5e-x| + c then

(int_{-1}^{1}) (frac { x^3+|x|+1 }{x^2+2|x|+1}) is equal to

The value of the integral (int_{1}^{2/3}) (frac { (x-x^3)^{1/3} }{x^4}) dx is

The value of (int_{-Ï€/2}^{Ï€/2}) (frac { sin^2 x }{1 + 2^x}) dx is

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(int_{-Ï€/2}^{Ï€/2}) (xÂ³ + x cos x + tan⁵ x + 1) dx is

âˆ«e^x(cos x – sin x)dx is equal to

âˆ«xÂ² e^xÂ³ dx equals

âˆ«e^x sec x (1 + tan x) dx equals

If I₄ + I₆ = a tan⁵ x + bx⁵ + c, where c is a constant of integration, then the ordered pair (a, b) is equal to

âˆ«tan^-1 âˆšx dx is equal to

If âˆ« (frac { 3e^x-5e^{-x} }{4r^x+5e^{-x}}) dx = ax + b log |4e^x + 5e^-x| + c then