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int(0)^(2pi) (sin 2 theta)/(a-b cos 2 th...

`int_(0)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta = `

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The value of the integral int_(0)^(2pi)(sin2 theta)/(a-b cos theta)d theta when a gt b gt 0 , is

[ (A) 8/5, (B) 5/8int_(0)^(2 pi)(sin2 theta)/(a-b cos theta)d theta equals- [ (A) 1, (B) 2, (C) pi/4]]

int _(0) ^(pi) sin ^(2) theta cos theta d theta

int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =

int_ (0) ^ (2 pi) e ^ (cos theta) cos (sin theta) d theta

If I_(n)=int_(0)^(2 pi)(cos(n theta))/(cos theta)d(theta), where n in N then.

int_(0)^( pi/2) sin^(2)theta cos theta d theta

The value of int_(0)^(pi//2)ln((sin^(2)theta)/(cos^(3)theta))d theta is

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then

A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
  1. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

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  2. Q. int0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I

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  3. int(0)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta =

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  4. Evaluate int0^1 log(1+x)/(1+x^2)dx

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  5. Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...

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  6. Evaluate the following: int0^(pi/2) |cosx-sinx|dx

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  7. Evaluate the following:int-2^2(|x|+|x-1|)dx

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  8. Prove that inta^b{[x]+[-x]}dx=a-b,where [x]is the greatest integer lex...

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  9. Statement-I int0^9[sqrtx]dx=13, Statement-II int0^(n^2) [sqrt x]dx=(n(...

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  10. Show that: int0^x[x]dx=[x]([x]-1)/2+[x](x-[x]), where [x] denotes the ...

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  11. The value of the integral overset(100pi)underset(0)int sqrt(1-cos2x)" ...

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  12. Evaluate the following : int(0)^(pi)(dx)/(1+sinx)

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  13. Evaluate the following:int0^(10pi)|cosx|dx

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  14. Evaluate int(0)^(npi+t)(|cosx|+|sinx|)dx, where n epsilonN and t epsil...

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  15. Show that: inta^bf(x)dx=int(a+c)^(b+c)f(x-c)dx and hence show that int...

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  16. If f(x) is a continuous function defined on [0,\ 2a]dot\ Then prove t...

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  17. If f(t) is an odd function, then varphi(x)=inta^xf(t)dx is an even fun...

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  18. It is known that f(x) is an odd function in the interval [p/2, p/2] an...

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  19. If f(a+x)=f(x), then prove that inta^(n a)f(x)dx=(n-1)int0^af(x)dx whe...

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  20. Evaluate: int0^(pi/2) (sin2x)/(sin^4x+cos^4x)dx

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