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The value of int( 0)^(pi//4) (pix-4x^(2)...

The value of `int_( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx` is

A

`(pi^(3))/(192)log_(e )2`

B

`(pi^(3))/(192)logsqrt(2)`

C

`(pi^(3))/(36)log 2`

D

`(pi^(3))/(48)logsqrt(2)`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If I=int(0)^(2pi) sin^(2) x" dx", then

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  2. If int(0)^(1) f(x)=M,int(0)^(1) g(x)dx=N, then which of the following ...

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  3. The value of int( 0)^(pi//4) (pix-4x^(2))log(1+tanx)dx is

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  4. The value of int(-pi//2)^(pi//2) sin{log(x+sqrt(x^(2)+1)}dx is

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  5. The value of int(0)^(2pi) cos^(99)x dx, is

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  6. If f(a+x)=f(x), then int(0)^(na) f(x)dx is equal to (n in N)

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  7. If f(t) is a continuous function defined on [a,b] such that f(t) is an...

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  8. If f(x) is an integrable function over every interval on the real line...

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  9. If I(1)=int(3pi)^(0) f(cos^(2)x)dx and I(2)=int(pi)^(0) f(cos^(2)x) th...

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  10. If f(x) is a quadratic polynomial in x such that 6int0^1 f(x)dx-{f(0...

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  11. The value of integral int(-2)^(4) x[x]dx is

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  12. If h(a)=h(b), the value of the integral inta^b [f(g(h(x))]^(-1)f'(g...

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  13. If F(x)=(1)/(x^(2))int(4)^(x) [4t^(2)-2F'(t)]dt then F'(4) equals

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  14. If f(x) is an odd function defined on [-T//2,T//2] and has period T, t...

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  15. If for every integer n, int(n)^(n+1) f(x)dx=n^(2), then the value of ...

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  16. int(-pi+4)^(pi//4) (tan^(2)x)/(1+a^(x))dx is equal to

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  17. The value of int(0)^(pi//2) cosec(x-pi//3)cosec(x-pi//6)dx is

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  18. The value of int(-1)^(1) x|x|dx, is

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  19. int0^3 |x^(3)+x^(2)+3x|dx is equal to

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  20. The value of the integral int(0)^(3) (dx)/(sqrt(x+1)+sqrt(5x+1)) is

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