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The value of the integral int0^(oo) log(...

The value of the integral `int_0^(oo) log(x+1/x) (dx)/(x^2 +1)` is

A

`pi log2`

B

`-pi log 2`

C

`(pi/2) log2`

D

`-(pi/2) log 2`

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  2. int0^(pi/4) (cos x- sin x) dx + int(pi/4)^((5pi)/4) (sinx-cosx) dx + i...

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  3. The value of the integral int0^(oo) log(x+1/x) (dx)/(x^2 +1) is

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  4. If f: R rarr R and g:R rarr R are one-to-one, real valued functions, t...

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  5. If int(log2)^(x) (du)/((e^(u)-1)^(1/2)) = pi/6, then e^(x) =

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  6. The value of int0^(sin^(2)theta) sin^(-1) sqrtphi dphi + int0^(cos^(2)...

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

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

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  9. int0^(sqrt2) [x^(2)] dx = , wher [x] is the greatest integer function

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  10. If P = int0^(3pi) f(cos^(2)x) dx and Q = int0^(pi) f(cos^(2)x) dx then

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  11. If int0^(1) (x^(7))/(sqrt(1-x^(4))) dx =

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  12. Let I(1) = inta^(pi-a) xf (sin x) dx, I(2) = inta^(pi-a) f(sinx) dx th...

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  13. The value of the integral int(1/n)^(((an-1))/(n)) sqrtx/(sqrt(a-x) + s...

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  14. For any integer n, the integral : int0^(pi) e^(cos^2) cos^(3) (2n + 1)...

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  15. If f(x) =

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  16. int(pi/6)^(pi/3) (dx)/(1+sqrtcotx) =

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  17. int(-pi)^(pi) (1 - x^2)sin x cdot cos^2 x cdot dx is :

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  18. If int0^(a) f(2a-x) dx = mu and int0^(a) f(x) dx = lambda, then int0^(...

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  19. If U(n) = int0^(pi/4) tan^(n) x dx then u(n)+u(n-2) =

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  20. The value of I = int0^(1) x|x-1/2|dx is

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