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

Q. `int_0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I`

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A DAS GUPTA-Properties and Application of definite Integrals-EXERCISE
  1. int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

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  2. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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