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Prove that: int0^(2pi)(xsin^(2n)x)/(s...

Prove that: `int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx`

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The correct Answer is:
`(pi^(2))`
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

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  2. int(1)^(e^(37))(pisin(pilogx))/(x)dx equals to.

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  3. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

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  4. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

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  5. The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equ...

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  6. The value of int(-2)^2|1-x^2|dx is

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  7. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  8. Match the conditions // expression in Column I with statement in Colum...

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  9. Match List I with List II and select the correct answer using the code...

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  10. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

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  11. Evaluate: int0^pie^(|cosx|)(2s in(1/2cosx)+3cos(1/2cosx))sinxdxdot

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  12. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

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  13. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

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  14. int(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to

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  15. Prove that int(0)^(1)tan^(-1)(1/(1-x+x^(2)))dx=2int(0)^(1)tan^(-1)xdx....

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  16. Evaluate int(0)^(pi//4) log (1+tan theta)d theta

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  17. about to only mathematics

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  18. Evaluate int(-1//sqrt(3))^(1//sqrt(3)) (x^(4))/(1-x^(4)) "cos"^(-1)((2...

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  19. Evaluate: int2^3(2x^5+x^4-2x^3+2x^2+1)/((x^2+1)(x^4-1))dx

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  20. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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