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Evaluate: int(-pi/2)^(pi/2)log((a-sin th...

Evaluate: `int_(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a >0`

A

0

B

1

C

2

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Exercise
  1. int(0)^(pi^(2)//4) sin sqrt(x)dx equals to

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  2. int(1//2)^(2) |log(10)x|dx equals to

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  3. Evaluate: int(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a ...

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  4. The value of the integral int(-pi//3)^(pi//3) (x sinx)/(cos^(2)x)dx, i...

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  5. The value of int(1)^(7sqrt(2)) (1)/(x(2x^(7)+1)dx is

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  6. The value of int(-1)^(3){|x-2|+[x]} dx, where [.] denotes the greatest...

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  7. If f(x)==|{:(sinx+sin2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,s...

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  8. Evaluate lim(xto oo) ((int(0)^(x)e^(x^(2))dx)^(2))/(int(0)^(x)e^(2x^(2...

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  9. The value of int(1)^(4) e^(sqrt(x))dx, is

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  10. The value of int(0)^(1000)e^(x-[x])dx, is ([.] denotes the greatest in...

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  11. The value of the integral int(0)^(100) sin(x-[x])pidx, is

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  12. The difference between the greatest and least values of the function p...

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  13. The value of int0^1 (2^(2x+1)-5^(2x-1))/(10^(x))dx is

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  14. The value of int(0)^(pi//2) (cos3x+1)/(2 cos x-1) dx is

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  15. The value of int(0)^(16pi//3) |sinx|dx is

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  16. If int(0)^(npi) f(cos^(2)x)dx=k int(0)^(pi) f(cos^(2)x)dx, then the va...

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  17. The value of int(-pi)^(pi) sinx f(cosx)dx is

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  18. If a lt int(0)^(2pi) (1)/(10+3 cos x)dx lt b. Then the ordered pair (a...

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  19. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dx ,is (a)0 (...

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  20. The value of the integral int(-pi//2)^(pi//2) sqrt(cosx-cos^(2)x)dx is

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