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The value of the integral int(-pi//2)^(p...

The value of the integral `int_(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi+x)) cos x dx `

A

0

B

`(pi ^(2))/(2) -4`

C

`(pi^(2))/(2 ) + 4`

D

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

Text Solution

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The correct Answer is:
B
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MOTION-DEFINITE INTEGRATION -EXERCISE -4 LEVEL-II
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  6. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

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  7. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  8. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

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  9. Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

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  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

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  11. Let f: RvecR be a continuous odd function, which vanishes exactly at o...

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  12. Let f (x) = 7 tan ^(8) x + 7 tan ^(6) x - 3 tan ^(4) x - 3 tan ^(2) x ...

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  13. Let f^(prime)(x)=(192 x^3)/(2+sin^4pix)fora l lx in Rw i t hf(1/2)=0....

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  14. Let F : R to R be a thrice differentiable function . Suppose that F(...

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  15. Let F : R to R be a thrice differentiable function . Suppose that F(...

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  16. The total number of distincts x in [0,1] for which int(0)^(x) (t^(2))...

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  17. Let f(x)=lim(n->oo)((n^n(x+n)(x+n/2)....(x+n/n))/(n!(x^2+n^2)(x^2+n^2/...

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  18. Let f: R -> R be a differentiable function such that f(0)=0, f((pi/2))...

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  19. For each positive integer n, let jy(n) =1/n ((n +1) (n +2) …(n +n) )...

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