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Prove that for any positive integer k ,...

Prove that for any positive integer `k ,(sin2k x)/(sinx)=2[cosx+cos3x++cos(2k-1)x]dot` Hence, prove that `int_0^(pi/2)sin2x kcotxdx=pi/2dot`

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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. about to only mathematics

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

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

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

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

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

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