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Evaluate : int0^(pi/2)(xsinxcosx)/(sin^4...

Evaluate : `int_0^(pi/2)(xsinxcosx)/(sin^4x+cos^4x)\ dx`

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The correct Answer is:
`I=(pi^(2))/(16)`
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. int0^1log(sqrt(1-x)+sqrt(1+x))dx equals:

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

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

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

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

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

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

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

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

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  10. about to only mathematics

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

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  12. Given a function f(x) such that It is integrable over every interval o...

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  13. For any real number x ,l e t[x] denote the largest integer less than o...

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

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  15. Let f be a non-negative function defined on the interval [0,1]. If int...

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  16. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

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  17. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

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  18. Consider the statements : P : There exists some x IR such that f(x)...

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  19. Let f (x)= int (x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = in...

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  20. Let f(x)=|secxcosx s e c^2x+cotx cos e c\ x cos^2x cos^2x cos e c^2x1c...

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