Integral Calculus Model Question Paper

11th Standard

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Maths

Time : 02:00:00 Hrs
Total Marks : 60
10 x 1 = 10
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. $\int {e^{6logx}-e^{5logx}\over e^{4logx}-e^{3logx}}dx$ is

(a)

x+c

(b)

${x^3\over 3}+c$

(c)

${3\over x^3}+c$

(d)

${1\over x^2}+c$

3. $\int tan^{-1}\sqrt{1-cos \ 2x\over 1+cos \ 2x}dx$ is

(a)

x2+c

(b)

2x2+c

(c)

${x^2\over2}+c$

(d)

$-{x^2\over2}+c$

4. $\int {sin^8x-cos^8x\over 1-2sin^2 \ x \ cos^2 \ x}dx$ is

(a)

${1\over2}sin 2x+c$

(b)

$-{1\over2}sin 2x+c$

(c)

${1\over2}cos 2x+c$

(d)

$-{1\over2}cos 2x+c$

5. $\int{x^2+cos^2x\over x^2+1}cosec^2xdx$ is

(a)

cot x+sin -1x+c

(b)

-cot x+tan-1x+c

(c)

-tan x+cot-1x+c

(d)

-cot x-tan-1x+c

6. $\int \sqrt{{1-x\over 1+x}}dx$ 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)

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

7. $\int {dx\over e^x-1}$is

(a)

$log|e^x|-log|e^x-1|+c$

(b)

$log|e^x|+log|e^x-1|+c$

(c)

$log|e^x-1|-log|e^x|+c$

(d)

$log|e^x+1|-log|e^x|+c$

8. $\int x^2e^{x\over2}dx$ is

(a)

$x^2e^{x\over2}-4xe^{x\over2}-8e^{x\over2}+c$

(b)

$2x^2e^{x\over2}-8xe^{x\over2}-16e^{x\over2}+c$

(c)

$2x^2e^{x\over2}-8xe^{x\over2}+16e^{x\over2}+c$

(d)

$x^2{e^{x\over2}\over 2}-{xe^{x\over2}\over 4}+{e^{x\over2}\over 8}+c$

9. $\int {x+2\over \sqrt{x^2+1}}dx$is

(a)

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

(b)

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

(c)

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

(d)

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

10. $\int e^{\sqrt{x}}dx$ is

(a)

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

(b)

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

(c)

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

(d)

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

11. 10 x 2 = 20
12. Integrate the following with respect to x. x10

13. Integrate the following with respect to x. ${1\over cos^2 \ x}$

14. Integrate the following with respect to x:${1\over 1+x^2}$

15. Integrate the following with respect to${1\over (3x-2)}$

16. If f '(x)=4x-5 and f(2)=1, find f(x).

17. Evaluate :$\int e^{xlog2}e^x dx$

18. Integrate the following functions with respect to x :(2x−5)(36+4x)

19. Integrate the following with respect to x eax cos bx

20. Evaluate the following integrals $\int{1\over (x+2)^2+1}dx$

21. $\frac { cosx }{ { sin }^{ 2 }x }$

22. 5 x 3 = 15
23. Integrate the following with respect to x: 123

24. Integrate the following functions with respect to x: e3x-6

25. Evaluate the following integrals:${15\over \sqrt{5x-4}}-8cot (4x+2)cosec(4x+2)$

26. Evaluate :$\int(tan \ x+cot \ x)^2dx$

27. Integrate the following functions with respect to x :${1+cos \ 4x \over cot \ x-tan \ x}$

28. 3 x 5 = 15
29. Integrate the following with respect to x:$(1+x^2)^{-1}$

30. A tree is growing so that, after t - years its height is increasing at a rate of ${18\over \sqrt{t}}$ cm per year Assume that when t = 0, the height is 5 cm. Find the height of the tree after 4 years

31. Integrate the following functions with respect to x :$x+1\over (x+2)(x+3)$