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Evaluate int(-1//sqrt(3))^(1//sqrt(3)) (...

Evaluate `int_(-1//sqrt(3))^(1//sqrt(3)) (x^(4))/(1-x^(4)) "cos"^(-1)((2x)/(1+x^(2)))dx`.

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The correct Answer is:
`I=(pi)/(12)[pi+3 ln (2+sqrt(3))-4sqrt(3)]`
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Evaluate int(0)^(pi//4) log (1+tan theta)d theta

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  2. about to only mathematics

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

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

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

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

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  7. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

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  8. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

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  9. The value of the integral overset(2a)underset(0)int (f(x))/(f(x)+f(2a-...

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  10. int0^1log(sqrt(1-x)+sqrt(1+x))dx equals:

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  11. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

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  12. Evaluate : int0^(pi/2)(xsinxcosx)/(sin^4x+cos^4x)\ dx

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  13. Evaluate: int0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

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  14. int(0)^(pi//4)(sin x + cos x)/(9+16 sin 2 x )

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  15. Show that int(0)^(pi)xf(sinx)dx=(pi)/2 int(0)^(pi)"fr"(sinx)dx.

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  16. Find the value of int(-1)^(3/2)|xsinpix|dx

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  17. Evaluate int(0)^(1)(tx+1-x)^(n)dx, where n is a positive integer a...

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  18. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

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  19. about to only mathematics

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  20. Show that int0^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integ...

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