Class 12 integration multiple choice question gmath

Multiple choice(Integtration)

integration multiple choice question

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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