#### Integral Calculus Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. If$\int f(x)dx=g(x)+c$ ,then$\int f(x)g'(x)dx$

(a)

$\int (f(x))^2dx$

(b)

$\int f(x)g(x)dx$

(c)

$\int f'(x)g(x)dx$

(d)

$\int (g(x))^2dx$

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

(a)

cot(xex)+c

(b)

sec(xex)+c

(c)

tan(xex)+c

(d)

cos(xex)+c

3. $\int {sec \ x\over \sqrt{cos 2x}}dx$ is

(a)

tan-1 (sin x)+c

(b)

2sin-1(tan x)+c

(c)

tan-1(cos x)+c

(d)

sin -1(tan x)+c

4. $\int{ {e^x}(x^2 \ tan^{-1}x+tan^{-1}x+1)\over x^2+1}dx$ is

(a)

ex tan-1(x+1)+c

(b)

tan-1(ex)+c

(c)

$e^x{(tan^{-1}x)^2\over 2}+c$

(d)

ex tan-1 x+c

5. $\int \sqrt{{1-x\over 1+x}}dx$ is

(a)

$\sqrt{1+x^2}+sin^{-1}x+c$

(b)

$sin^{-1}x-\sqrt{1+x^2}+c$

(c)

$log|x+\sqrt{1-x^2}|-\sqrt{1-x^2}+c$

(d)

$\sqrt{1-x^2}+log|x+\sqrt{1-x^2}|+c$

6. 3 x 2 = 6
7. Integrate the following with respect to x.${sin \ x \over cos ^2 \ x}$

8. Integrate the following with respect to x: x11

9. Integrate the following with respect to x:${1\over \sqrt{1-25 x^2}}$

10. 3 x 3 = 9
11. Integrate the following functions with respect to x: cos (5-11x)

12. If f '(x)=3x2-4x+5 and f(1)=3, then find f(x).

13. Evaluate :$\int {3x+7\over x^2-3x+2}dx$

14. 2 x 5 = 10
15. Integrate the following functions with respect to x:${1\over \sqrt{1-81x^2}}$

16. Integrate the following functions with respect to x :${8^{1+x}+4^{1-x}\over 2^x}$