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Evaluate: int0^pi(xsin2xsin(pi/2cosx))/(...

Evaluate: `int_0^pi(xsin2xsin(pi/2cosx))/(2x-pi)dx`

A

`(8)/(pi^(2))`

B

`(2)/(pi)`

C

`(1)/(pi^(2))`

D

none

Text Solution

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The correct Answer is:
A
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ML KHANNA-DEFINITE INTEGRAL-Problem set (3) (Multiple Choice Questions)
  1. int(-pi)^(pi) (2x(1+ sinx))/(1+ cos^(2))dx is

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  2. overset(-pi//2)underset(-3pi//2)int{(x+pi)^(3)+cos^(2)(x+3pi)}dx, is

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  3. Evaluate: int0^pi(xsin2xsin(pi/2cosx))/(2x-pi)dx

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  4. Evaluate the following definite integral: int(-sqrt(2))^(sqrt(2))(2...

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  5. The value of int(-2)^(2) (ax^(3) + bx+ c) dx depends on which followin...

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  6. If f(x)= ax^(2) +bx +c such that f(0)=2 f'(0)= -3, f''(0) =4, then int...

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  7. int(-pi//2)^(pi//2) sin^(2) x cos^(2) x (sin x +cos x) dx=

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  8. The value of the integral int(-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx

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  9. The integral value of int(-2)^(0) [x^(3)+3x^(2) +3x +3+ (x+1) cos (x+1...

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  10. The value of the integral int(-pi//4)^(pi//4) (1)/(sin^(4) x) dx is

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  11. The value of the integral overset(1//2)underset(-1//2)int {((x+1)/(...

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  12. The value of the integral int(-1)^(1) log (x+ sqrt(x^(2)+1)) dx is

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  13. The value of overset(pi//2)underset(-pi//2)int sin{log(x+sqrt(x^(2)+1)...

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  14. int(log 1//2)^(log 2) sin {(e^(x)-1)/(e^(x) +1}dx=

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  15. The value of overset(1//2)underset(-1//2)int |xcos((pix)/(2))|dx is

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  16. The function F(x)= int(0)^(x) log (t+ sqrt(1+t^(2)))dt is

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  17. The function F(x)= int(0)^(pi) "log" ((1-x))/((1+x)) dx is a function ...

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  18. The antiderivative of every odd function is an

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  19. If n in N, then int(-n)^(n) (-1)^([x]) dx equals

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  20. int(-1)^(1) (sqrt(1+x+x^(2))-sqrt(1-x+x^(2))) dx =

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