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int0^(oo) (xdx)/((1+x)(1+x^(2))) =...

`int_0^(oo) (xdx)/((1+x)(1+x^(2))) =`

A

`pi/2`

B

0

C

1

D

`pi/4`

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The correct Answer is:
D
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  2. int0^(2pi) (sinx+|sinx|) dx =

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  3. int0^(oo) (xdx)/((1+x)(1+x^(2))) =

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  4. int0^(pi/8) cos^(3) 4 theta d theta =

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  5. int(pi/4)^(pi/2) cosec^(2)x dx =

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  6. If I(1)= int(0)^(pi//2) x sin x dx and I(2)=int(0)^(pi//2) x cos x dx,...

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  7. If f (x) is defined [-2, 2] by f(x)=4x^(2)-3x+1 and g(x)=(f(-x)-f(x))...

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  8. If k int (0)^(1)x.f(3x)dx = int(0)^(3) t. f(t)dt, then the value of k ...

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  9. The value of the integral int0^(pi//2) (sin^(100) x - cos^(100) x) dx ...

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  10. int(1)^(3)(x-1)(x-2)(x-3)dx=

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  11. If 2f(x)- 3f(1/x) = x then int1^(e) f(x) dx =

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  12. If [x] denote the greatest integer function , then , int(0)^(pi//6) (1...

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  13. The value of the integral, int3^6 (sqrt(x))/(sqrt(9 - x) + sqrt(x))dx ...

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  14. int0^(10pi) |sin x| dx is

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  15. int(-pi)^(pi) (2x(1 + sin x))/(1 + cos^2 x) dx is :

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  16. If In = int0^(pi//4) tan^n x dx, then lim(n to oo) n [In + I(n -2)] eq...

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  17. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

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  18. The value of the integral I = int0^1 x (1 - x)^(n) dx is :

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  19. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

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  20. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

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