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Class 12 integration multiple choice question gmath

Multiple choice(Integtration)

Choose and write the correct option in the following question:(integration multiple choice question)

1.) $\int x^2e^{x^3} dx$ is equal to

(a) $\frac{1}{3}e^{x^3}+C$ (b) $\frac{1}{3}e^{x^4}+C$

(c) $\frac{1}{2}e^{x^3}+C$ (d) $\frac{1}{2}e^{x^2}+C$

Answer (a)

2.) $\int \frac{e^x(1+x)}{\cos^2(xe^x)}dx$ is equal to

(a) $\tan{(xe^x)}+C$ (b) $\cot{(xe^x)}+C$

(c) $\cot(e^x)+C$ (d) $\tan[e^x(1+x)]+C$

Answer (a)

3.) $\int e^x(\cos x - \sin x)dx$ is equal to

(a) $e^x\cos x+C$ (b) $e^x\sin x + C$

(c) $-e^x\cos x+C$ (d) $-e^x\sin x+C$

Answer (a)

4.) $\int\frac{dx}{\sin^2x.\cos^2x}$ is equal to

(a) $\tan x+\cot x+C$ (b) $(\tan x+\cot x)^2+C$

(c) $\tan x - \cot x+C$ (d) $(\tan x-\cot x)^2 + C$

Answer (c)

5.) If $\int\frac{3e^x-5e^{-x}}{4e^x+5e^{-x}}dx = ax + b\log|4e^x + 5e^{-x}|+C$

(a) a = -1/8, b = 7/8 (b) a = 1/8, b = 7/8

(c) a = -1/8, b = -7/8 (d) a = 1/8, b = -7/8

Answer (a)

6.) The value of $\displaystyle \int_{-\pi/2}^{\pi/2}(x^3+x\cos x+\tan^5x+1)dx$ is

(a) 0 (b) 2

(c) π (d) 1

Answer (c)

7.) $\displaystyle \int\frac{dx}{\sin(x-a)\sin(x+a)}$ is equal to

(a) $\sin(b-a)\log|\frac{\sin(x-b)}{\sin(x-a)}|+C$

(b) $\operatorname{cosec(b-a)}\log|\frac{\sin(x-a)}{\sin(x-b)}|+C$

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

(d) $\sin(b-a)\log|\frac{\sin(x-a)}{\sin(x-b)}|+C$

Answer (c)

8.) $\displaystyle \int \tan^{-1}\sqrt{x}dx$ is equal to

(a) $(x+1)\tan^{-1}\sqrt{x}-\sqrt{x} +C$

(b) $x\tan^{-1}\sqrt{x}-\sqrt{x} +C$

(c) $\sqrt{x}-x\tan^{-1}\sqrt{x} +C$

(d) $\sqrt{x}-(x+1)\tan^{-1}\sqrt{x} +C$

Answer (a)

9.) $\displaystyle \int e^x(\frac{1-x}{1+x^2})^2dx$ 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)

10.) $\displaystyle \int \frac{\sin^6x}{\cos^8x}dx$ is equal to

(a) $\frac{\tan^6x}{5}+C$ (b) $\frac{\tan^7x}{5}+C$

(c) $\frac{\tan^7x}{7}+C$ (d) None of these

Answer (c)

11.) If $\displaystyle \int\frac{x^3}{\sqrt{1+x^2}}dx = a(1+x^2)^{3/2}+b\sqrt{1+x^2}+C$ , then

(a) a = 1/3, b = 1 (b) a = -1/3, b = 1

(c) a = -1/3, b = -1 (c) a = 1/3, b = -1

Answer (d)

12.) The integral $\displaystyle \int\frac{x^9}{(4x^2+1)^6}dx$ is equal to

(a) $\frac{1}{5x}(4+\frac{1}{x^2})^{-5}+C$

(b) $\frac{1}{5}(4+\frac{1}{x^2})^{-5}+C$

(c) $\frac{1}{10x}(5)^{-5}+C$

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

Answer (d)

13.) $\displaystyle \int\tan^2(2x) dx$ is equal to

(a) $\frac{4-\pi}{8}$ (b) $\frac{4+\pi}{8}$

(c) $\frac{4-\pi}{4}$ (d) $\frac{4-\pi}{2}$

Answer (a)

14.) $\displaystyle \int_{a+c}^{b+c} f(x) dx$ is equal to

(a) $\int _ a^b f(x-c)dx$ (b) $\int_a^bf(x+c)dx$

(c) $\int_a^bf(x) dx$ (d) $\int_{a-c}^{b-c} f(x)dx$

Answer (b)

15.) If f and g are continuous functions in [0, 1] satisfying f(x) = f(a-x) and g(x) +g(a-x) = a, then $\int_0^af(x).g(x)dx$ is equal to

(a) a/2 (b) $\frac{a}{2}\int_0^af(x) dx$

(c) $\int_0^af(x) dx$ (d) $a\int_0^af(x)dx$

Answer (b)

16.) $\displaystyle\int_{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1}dx$ is equal to

(a) $\log 2$ (b) $2\log 2$

(c) $\frac{1}{2}\log 2$ (d) $4\log 2$

Answer (b)

17.) $\int_0^1\frac{e^t}{1+t}dt = a$ , then $\int_0^1\frac{e^t}{(1+t)^2}dt$ is equal to

(a) a – 1 + e/2 (b) a + 1 – e/2

(c) a – 1 – e/2 (d) a + 1 + e/2

Answer (b)

18.) $\int_{-2}^2|x\cos \pi x|dx$ is equal to

(a) 8/π (b) 4/π

(c) 2/π (d) 1/π

Answer (a)

19.) The integral value of $\displaystyle \int_0^{\pi/2}\frac{\tan x}{1+m^2\tan^2x}dx m>0$ , is

(a) $\frac{\log m}{(m^2-1)}$ (b) $\log(\frac{m^2-m}{2})$

(c) $\log 3m$ (d) 0

Answer (a)

20.) $\int_{-1}^2|x|dx$ is equal to

(a) 1 (b) 3/2

(c) 2 (d) 5/2

Answer (d)

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