Check the below NCERT MCQ Questions for Class 12 Maths Chapter 7 Integrals with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Integrals Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Integrals Class 12 MCQs Questions with Answers

Integration MCQ Class 12 Chapter 7 Question 1.
$$\int \frac{x+\sin x}{1+\cos x}$$ dx is equal to
(a) log |1 + cos x | + c
(b) log | x + sin x | + c
(c) x – tan + c
(d) x. tan $$\frac{x}{2}$$ + c

Answer: (d) x. tan $$\frac{x}{2}$$ + c

MCQ On Integration Class 12 Chapter 7 Question 2.
∫1.dx =
(a) x + k
(b) 1 + k
(c) $$\frac{x^2}{2}$$ + k
(d) log x + k

Integration MCQ Questions Class 12 Chapter 7 Question 3.
∫$$\frac{dx}{√x}$$ =
(a) √x + k
(b) 2√x + k
(c) x + k
(d) $$\frac{2}{3}$$x3/2 + k

MCQ On Integration Class 12 Chapter 7 Question 4.
∫$$\frac{dx}{1+cos x}$$ =
(a) tan $$\frac{x}{2}$$ + k
(b) $$\frac{1}{2}$$ tan $$\frac{x}{2}$$ + k
(c) 2 tan $$\frac{x}{2}$$ + k
(d) tan² $$\frac{x}{2}$$ + k

Answer: (a) tan $$\frac{x}{2}$$ + k

Integration MCQs With Answers Pdf Class 12 Chapter 7 Question 5.
$$\int_{a}^{b}$$ x5 dx =
(a) tan $$\frac{x}{2}$$ + k
(b) $$\frac{1}{2}$$ tan $$\frac{x}{2}$$ + k
(c) 2 tan $$\frac{x}{2}$$ + k
(d) tan² $$\frac{x}{2}$$ + k

Answer: (a) tan $$\frac{x}{2}$$ + k

Integration MCQ With Answers Class 12 Chapter 7 Question 6.
If x > a, ∫$$\frac{dx}{x^2-a^2}$$ =
(a) $$\frac{2}{2a}$$ log $$\frac{x-a}{x+a}$$ + k
(b) $$\frac{2}{2a}$$ log $$\frac{x+a}{x-a}$$ + k
(c) $$\frac{1}{a}$$ log(x² – a²) + k
(d) log(x + $$\sqrt{x^2-a^2}$$ + k)

Answer: (a) $$\frac{2}{2a}$$ log $$\frac{x-a}{x+a}$$ + k

Integration Objective Questions Class 12 Chapter 7 Question 7.
∫$$\frac{cos 2x dx}{(sinx+cosx)^2}$$ =
(a) –$$\frac{1}{sinx+cosx}$$ + c
(b) log | sin x + cos x | + c
(c) log | sin x – cos x | + c
(d) $$\frac{1}{(sinx+cosx)^2}$$

Answer: (b) log | sin x + cos x | + c

MCQ On Integration With Answers Class 12 Chapter 7  Question 8.
∫$$\frac{(1+logx)^2}{1+x^2}$$ dx =
(a) $$\frac{1}{3}$$(1+log)³ + c
(b) $$\frac{1}{2}$$(1+log)² + c
(c) log (log 1 + x) + 2
(d) None of these

Answer: (a) $$\frac{1}{3}$$(1+log)³ + c

Integration MCQs Class 12 Chapter 7  Question 9.
$$\int_{0}^{1}\frac{(tan^{-1}x)^2}{1+x^2}$$ dx =
(a) 1
(b) $$\frac{π^2}{64}$$
(c) $$\frac{π^2}{192}$$
(d) None of these

Answer: (c) $$\frac{π^2}{192}$$

MCQ Of Integration Class 12 Chapter 7 Question 10.
$$\int_{-2}^{2}$$ |x|dx =
(a) 0
(b) 2
(c) 1
(d) 4

MCQs On Integration Class 12 Chapter 7 Question 11.
∫$$\frac{x^4+1}{x^2+1}$$ dx is equal to
(a) $$\frac{x^3}{3}$$ + x + tan-1 x + c
(b) $$\frac{x^3}{3}$$ – x + tan x + c
(c) $$\frac{x^3}{3}$$ + x + 2tan-1 x + c
(d) $$\frac{x^3}{3}$$ – x + 2tan-1 x + c

Answer: (d) $$\frac{x^3}{3}$$ – x + 2tan-1 x + c

Integration MCQ With Answers Pdf Class 12 Chapter 7 Question 12.
∫(√x + $$\frac{1}{√x}$$) dx =
(a) $$\frac{1}{x}$$ x$$\frac{1}{3}$$ + 2x$$\frac{1}{2}$$ + c
(b) $$\frac{2}{3}$$ x$$\frac{2}{3}$$ + $$\frac{1}{2}$$x2 + c
(c) $$\frac{2}{3}$$ x$$\frac{3}{2}$$ + 2x$$\frac{1}{2}$$ + c
(d) $$\frac{3}{2}$$ x$$\frac{3}{2}$$ + $$\frac{1}{2}$$x$$\frac{1}{2}$$ + c

Answer: (c) $$\frac{2}{3}$$ x$$\frac{3}{2}$$ + 2x$$\frac{1}{2}$$ + c

Integration MCQ Questions And Answers Class 12 Chapter 7  Question 13.
∫$$\frac{sin^2x-cos^2x}{sin^2xcos^2x}$$ dx is equal to
(a) tan x + cos x + c
(b) tan x + cosec x + c
(c) tan x + cot x + c
(d) tan x+ sec x + c

Answer: (c) tan x + cot x + c

Integral MCQ Questions Class 12 Chapter 7 Question 14.
$$\frac{d}{dx}$$∫f(x)dx is equal to
(a) f'(x)
(b) f(x)
(c) f'(x’)
(d) f(x) + c

MCQ Integration Class 12 Chapter 7 Question 15.
∫$$\frac{xdx}{(x-1)(x-2)}$$ equals

(d) log |(x – 1)(x – 2) + c

Answer: (b) log|$$\frac{(x-2)^2}{x-2}$$| + c

Integration MCQs With Answers Chapter 7  Question 16.
What is the value of $$\int_{0}^{\pi / 2}$$ $$\frac{\sqrt{tan x}}{\sqrt{tan x}+\sqrt{cot x}}$$ dx?
(a) $$\frac{π}{2}$$
(b) $$\frac{π}{4}$$
(c) $$\frac{π}{8}$$
(d) None of these

Answer: (b) $$\frac{π}{4}$$

Integrals MCQs Class 12 Chapter 7 Question 17.
What is the value of $$\int_{0}^{\pi / 2}$$ $$\frac{sinx – cos x}{1+sin xcos x}$$ dx?
(a) 1
(b) $$\frac{π}{2}$$
(c) 0
(d) –$$\frac{π}{2}$$

Integration MCQs Class 12 Chapter 7 Question 18.
What is the value of $$\int_{\pi / 6}^{\pi / 3}$$ $$\frac{dx}{sin2x}$$?
(a) $$\frac{1}{2}$$ log(-l)
(b) log(- 1)
(c) log 3
(d) log √3

Integration MCQ Class 12 Question 19.
What is the value of $$\int_{-1}^{1}$$ sin³ x cos² xdx?
(a) 0
(b) 1
(c) $$\frac{1}{2}$$
(d) 2

MCQ Questions On Integration Question 20.
What is the value of $$\int_{1}^{e} \frac{1+\log x}{x}$$ dx?
(a) $$\frac{3}{2}$$
(b) $$\frac{1}{2}$$
(c) e
(d) $$\frac{1}{e}$$

Answer: (a) $$\frac{3}{2}$$

Question 21.
$$\int_{-\pi / 2}^{\pi / 2}$$ sin9 xdx =
(a) -1
(b) 0
(c) 1
(d) None of these

Question 22.
$$\int_{0}^{\pi^{2} / 4} \frac{\sin \sqrt{y}}{\sqrt{y}}$$
(a) 1
(b) 2
(c) $$\frac{π}{4}$$
(d) $$\frac{π^2}{8}$$

Question 23.
$$\int_{0}^{\infty} \frac{1}{1+e^{x}}$$ dx =
(a) log 2
(b) -log 2
(c) log 2 – 1
(d) log 4 – 1

Question 24.
$$\int_{0}^{1}$$ x(1 – x)99 is equal to
(a) $$\frac{1}{10010}$$
(b) $$\frac{1}{10100}$$
(c) $$\frac{1}{1010}$$
(d) $$\frac{11}{10100}$$

Answer: (b) $$\frac{1}{10100}$$

Question 25.
What is the value of $$\int_{0}^{1}$$ $$\frac{d}{dx}$${sin-1($$\frac{2x}{1+x^2}$$)}dx?
(a) 0
(b) π
(c) -π
(d) $$\frac{π}{2}$$

Answer: (d) $$\frac{π}{2}$$

Question 26.
$$\int_{0}^{1}$$ $$\frac{x}{1+x}$$ dx =
(a) 1 – log 2
(b) 2
(c) 1 + log 2
(d) log 2

Answer: (a) 1 – log 2

Question 27.
∫$$\frac{sin x + cos x}{\sqrt{1+2sin x}}$$ dx =
(a) log(sin x – cos x)
(b) x
(c) log x
(d) log sin (cos x)

Question 28.
∫log10 xdx =
(a) loge 10.x loge ($$\frac{x}{e}$$) + c
(b) log10 e.x loge ($$\frac{x}{e}$$) + c
(c) (x – 1) loge x + c
(d) $$\frac{1}{x}$$ + c

Answer: (b) log10 e.x loge ($$\frac{x}{e}$$) + c

Question 29.
∫($$\frac{cos 2θ – 1}{cos 2θ + 1}$$) dθ =
(a) tan θ – θ + c
(b) θ + tan θ + c
(c) θ – tan θ + c
(d) -θ – cot θ + c

Answer: (c) θ – tan θ + c

Question 30.
∫$$\frac{2dx}{\sqrt{1-4x^2}}$$ =
(a) tan-1 (2x) + c
(b) cot-1 (2x) + c
(c) cos-1 (2x) + c
(d) sin-1 (2x) + c

Answer: (d) sin-1 (2x) + c

Question 31.
Value of ∫$$\frac{dx}{\sqrt{2x – x^2}}$$
(a) sin-1 (x – 1) + c
(b) sin-1 (1 + x) + c
(c) sin-1 (1 + x²) + c
(d) –$$\sqrt{2x-x^2}$$ + c

Answer: (a) sin-1 (x – 1) + c

Question 32.
∫x² sin x³ dx =
(a) $$\frac{1}{3}$$ cos x³ + c
(b) –$$\frac{1}{3}$$ cos x + c
(c) $$\frac{-1}{3}$$ cos x³ + c
(d) $$\frac{1}{2}$$ sin² x³ + c

Answer: (c) $$\frac{-1}{3}$$ cos x³ + c

Question 33.
∫$$\frac{cos 2x- cos 2θ}{cos x – cos θ}$$dx is equal to
(a) 2 (sin x + x cos θ) + C
(b) 2 (sin x – x cos θ) + C
(c) 2 (sin x + 2x cos θ) + C
(d) 2 (sin x – 2x cos θ) + C

Answer: (a) 2 (sin x + x cos θ) + C

Question 34.
∫$$\frac{dx}{sin(x-a)sin(x-b)}$$ is equal to
(a) sin(b – a) log |$$\frac{sin (x-b)}{sin(x-a)}$$| + C
(b) cosec (b – a) log |$$\frac{sin (x-b)}{sin(x-b)}$$| + C
(c) cosec (b – a) log |$$\frac{sin (x-b)}{sin(x-a)}$$| + C
(d) sin (b – a) log |$$\frac{sin (x-a)}{sin(x-b)}$$| + C

Answer: (c) cosec (b – a) log |$$\frac{sin (x-b)}{sin(x-a)}$$| + C

Question 35.
∫tan-1 √xdx is equal to
(a) (x + 1)tan-1 √x – √x + C
(b) x tan-1 √x – √x + C
(c) √x – x tan-1 √x + C
(d) √x – (x + 1)tan-1 √x + C

Answer: (a) (x + 1)tan-1 √x – √x + C

Question 36.
∫ex($$\frac{1-x}{1+x^2}$$)² dx is equal to
(a) $$\frac{e^x}{1+x^2}$$ + C
(b) –$$\frac{-e^x}{1+x^2}$$ + C
(c) $$\frac{e^x}{(1+x^2)^2}$$ + C
(d) $$\frac{-e^x}{(1+x^2)^2}$$ + C

Answer: (a) $$\frac{e^x}{1+x^2}$$ + C

Question 37.
∫$$\frac{x^9}{(4x^2+1)^6}$$ dx is equal to

Answer: (d) $$\frac{1}{10}$$ ($$\frac{1}{x^2}$$ + 4)-5 + C

Question 38.
If ∫$$\frac{dx}{(x+2)(x^2+1)}$$ = a log |1 + x²| + b tan-1 x + $$\frac{1}{5}$$ log |x + 2| + C, then
(a) a = $$\frac{-1}{10}$$, b = $$\frac{-2}{5}$$
(b) a = $$\frac{1}{10}$$, b = $$\frac{-2}{5}$$
(c) a = $$\frac{-1}{10}$$, b = $$\frac{2}{5}$$
(d) a = $$\frac{1}{10}$$, b = $$\frac{2}{5}$$

Answer: (c) a = $$\frac{-1}{10}$$, b = $$\frac{2}{5}$$

Question 39.
∫ $$\frac{x^3}{x+1}$$ is equal to
(a) x + $$\frac{x^2}{2}$$ + $$\frac{x^3}{3}$$ – log |1 – x| + C
(b) x + $$\frac{x^2}{2}$$ – $$\frac{x^3}{3}$$ – log |1 – x| + C
(c) x + $$\frac{x^2}{2}$$ – $$\frac{x^3}{3}$$ – log |1 + x| + C
(d) x + $$\frac{x^2}{2}$$ + $$\frac{x^3}{3}$$ – log |1 + x| + C

Answer: (d) x + $$\frac{x^2}{2}$$ + $$\frac{x^3}{3}$$ – log |1 + x| + C

Question 40.
If ∫$$\frac{x^3dx}{\sqrt{1+x^2}}$$ = a(1 + x²)3/2 + b$$\sqrt{1 + x^2}$$ + C, then
(a) a = $$\frac{1}{3}$$, b = 1
(b) a = $$\frac{-1}{3}$$, b = 1
(c) a = $$\frac{-1}{3}$$, b = -1
(d) a = $$\frac{1}{3}$$, b = -1

Answer: (d) a = $$\frac{1}{3}$$, b = -1

Question 41.
$$\int_{-\pi / 4}^{\pi / 4}$$ $$\frac{dx}{1+cos 2x}$$ dx is equal to
(a) 1
(b) 2
(c) 3
(d) 4

Question 42.
$$\int_{0}^{\pi / 2}$$ $$\sqrt{1+sin 2x}$$ dx is equal to
(a) 2√2
(b) 2(√2 + 1)
(c) 0
(d) 2(√2 – 1)

Question 43.
Evaluate: ∫(2 tan x – 3 cot x)² dx
(a) -4tan x – cot x – 25x + C
(b) 4 tan x – 9 cot x – 25x + C
(c) – 4 tan x + 9 cot x + 25x + C
(d) 4 tan x + 9 cot x + 25x + C

Answer: (b) 4 tan x – 9 cot x – 25x + C

Question 44.
Evaluate: ∫ sec²(7 – 4x)dx
(a) –$$\frac{1}{4}$$ tan(7 – 4x) + C
(b) $$\frac{1}{4}$$ tan(7 – 4x) + C
(c) $$\frac{1}{4}$$ tan(7 + 4x) + C
(d) –$$\frac{1}{4}$$ tan(7x – 4) + C

Answer: (a) –$$\frac{1}{4}$$ tan(7 – 4x) + C

Question 45.
∫ $$\frac{10x^9+10^xlog_e 10}{10^x+x^{10}}$$ dx is equal to
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10)-1 + C
(d) loge(10x + x10) + C

Answer: (d) loge(10x + x10) + C

Question 46.
Evaluate: ∫ sec4/3 x cosec8/3 xdx
(a) $$\frac{3}{5}$$ tan-5/3 x – 3 tan1/3 x + C
(b) –$$\frac{3}{5}$$ tan-5/3 x + 3 tan1/3 + C
(c) –$$\frac{3}{5}$$ tan-05/3 x – 3 tan1/3 + C
(d) None of these

Answer: (b) –$$\frac{3}{5}$$ tan-5/3 x + 3 tan1/3 + C

Question 47.
∫ $$\frac{a}{(1+x^2)tan^{-1}x}$$ dx =
(a) a log |tan-1 x| + C
(b) $$\frac{1}{2}$$(tan-1 x)² + C
(c) a log (1 + x2) + C
(d) None of these

Answer: (a) a log |tan-1 x| + C

Question 48.
∫ $$\frac{cot x}{\sqrt[3]{sin x}}$$ dx =
(a) $$\frac{-3}{\sqrt[3]{sin x}}$$ + C
(b) $$\frac{-2}{sin^3 x}$$ + C
(c) $$\frac{3}{sin^{1/3}x}$$ + C
(d) None of these

Answer: (a) $$\frac{-3}{\sqrt[3]{sin x}}$$ + C

Question 49.
Evaluate: ∫ $$\frac{1}{1+3sin^2x+8cos^2x}$$ dx
(a) $$\frac{1}{6}$$ tan-1 (2 tan x) + C
(b) tan-1 (2 tan x) + C
(c) $$\frac{1}{6}$$ tan-1($$\frac{2 tan x}{3}$$) + C
(d) None of these

Answer: (c) $$\frac{1}{6}$$ tan-1($$\frac{2 tan x}{3}$$) + C

Question 50.
Evaluate: ∫ $$\frac{1}{\sqrt{9+8x-x^2}}$$ dx
(a) -sin-1 ($$\frac{x-4}{5}$$) + C
(b) sin-1 ($$\frac{x+4}{5}$$) + C
(c) sin-1 ($$\frac{x-4}{5}$$) + C
(d) None of these

Answer: (c) sin-1 ($$\frac{x-4}{5}$$) + C

Question 51.
∫ $$\frac{dx}{1-cosx-sinx}$$ is equal to
(a) log |1 + cot$$\frac{x}{2}$$| + C
(b) log |1 – tan$$\frac{x}{2}$$| + C
(c) log |1 – cot$$\frac{x}{2}$$| + C
(d) log |1 + tan$$\frac{x}{2}$$| + C

Answer: (c) log |1 – cot$$\frac{x}{2}$$| + C

Question 52.
Evaluate: ∫ $$\frac{1}{\sqrt{1-e^{2x}}}$$ dx
(a) log |e-x + $$\sqrt{e^{-2x} – 1}$$| + C
(b) -log |e-x + $$\sqrt{e^{-2x} – 1}$$| + C
(c) -log |e-x – $$\sqrt{e^{-2x} – 1}$$| + C
(d) None of these

Answer: (b) -log |e-x + $$\sqrt{e^{-2x} – 1$$| + C

Question 53.
If ∫ $$\frac{3x+4}{x^3-2x-4}$$ dx = log |x – 2| + k log f(x) + c, then
(a) f(x) = |x² + 2x + 2|
(b) f(x) = x² + 2x + 2
(c) k = –$$\frac{1}{2}$$
(d) All of these

Question 54.
Evaluate: ∫ $$\frac{1-cosx}{cosx(1+cosx)}$$ dx
(a) log|sec x + tan x| – 2 tan(x/2) + C
(b) log|sec x – tan x| – 2 tan(x/2) + C
(c) log|sec x + tan x| + 2 tan(x/2) + C
(d) None of these

Answer: (a) log|sec x + tan x| – 2 tan(x/2) + C

Question 55.
∫ cos(loge.x)dx is equal to
(a) $$\frac{1}{2}$$ x[cos (logex) + sin(logex)]
(b) x[cos (logex) + sin(logex)]
(c) $$\frac{1}{2}$$ x[cos (logex) – sin(logex)]
(d) x[cos (logex) – sin(logex)]

Answer: (b) –$$\frac{3}{5}$$ tan-5/3 x + 3 tan1/3 + C

Question 56.
∫ |x| dx is equal to
(a) $$\frac{1}{2}$$ x² + C
(b) –$$\frac{x^2}{2}$$ + C
(c) x|x| + C
(d) $$\frac{1}{2}$$ x|x| + C

Answer: (d) $$\frac{1}{2}$$ x|x| + C

Question 57.
∫ sin-1 xdx is equal to
(a) cos-1 x + C
(b) x sin-1x + $$\sqrt{1-x^2}$$ + C
(c) $$\frac{1}{\sqrt{1-x^2}}$$ + C
(d) x sin-1x – $$\sqrt{1-x^2}$$ + C

Answer: (b) x sin-1x + $$\sqrt{1-x^2}$$ + C

Question 58.
∫ cos-1($$\frac{1}{x}$$)dx equals
(a) x sec-1 x + log |x + $$\sqrt{x^2-1}$$| + C
(b) x sec-1 x – log |x + $$\sqrt{x^2-1}$$| + C
(c) -x sec-1 x – log |x + $$\sqrt{x^2-1}$$| + C
(d) None of these

Answer: (b) x sec-1 x – log |x + $$\sqrt{x^2-1}$$| + C