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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:
`(pi^(2))/(16)`
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. Show that int(0)^(pi)xf(sinx)dx=(pi)/2 int(0)^(pi)"fr"(sinx)dx.

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  2. about to only mathematics

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

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  4. Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx

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  5. Evaluate the following definite integral: int(-sqrt(2))^(sqrt(2))(2...

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  6. Evaluate int(-2)^(2)(d x)/(4+ x^(2))directly as well as by

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  7. If int(a)^(b)f(dx)dx=l(1), int(a)^(b)g(x)dx = l(2) then :

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  8. (1)/(c )int(ac)^(bc)f((x)/(c ))dx=

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  9. int(0)^(pi//2n)(dx)/(1+(tan nx)^(n)) is equal to n in N :

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  10. overset(pi//2)underset(-pi//2)int (cos x)/(1+e^(x))dx=

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  11. int(0)^(2pi)[|sin x|+|cos x|]dx, where [.] denotes the greatest intege...

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  12. If f(pi)=2 and int(0)^(pi)(f(x)+f''(x))sin x dx=5, then f(0) is equal ...

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  13. If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then underset(...

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  14. Evaluate: int0^(4pi)(dx)/(cos^2x(2+tan^2x)

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  15. The value of int(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greate...

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  16. The value of int(1)^(4){x}^([x]) dx (where , [.] and {.} denotes the g...

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  17. If f(x) is continuous for all real values of x , then sum(r=1)^nint0^...

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  18. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

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  19. int(-pi/2)^(pi/2)(e^(|sinx|)cosx)/((1+e^(tanx))dx is equal to e+1 ...

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  20. The value of int(0)^(2)[x^(2)-1]dx, where [x] denotes the greatest in...

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