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If fa n dg are continuous function on [0...

If `fa n dg` are continuous function on `[0,a]` satisfying `f(x)=f(a-x)a n dg(x)(a-x)=2,` then show that `int_0^af(x)g(x)dx=int_0^af(x)dxdot`

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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Evaluate: int0^pi(xsin2xsin(pi/2cosx)/(2x-pi)dx

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

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

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

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

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

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

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

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

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

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

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

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

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  14. about to only mathematics

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

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

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

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

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

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

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