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The value of int(0)^(oo) (dx)/((x^(2)+4)...

The value of `int_(0)^(oo) (dx)/((x^(2)+4)(x^(2)+9) )` is

A

`(pi)/(60)`

B

`(pi)/(20)`

C

`(pi)/(40)`

D

`(pi)/(80)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` l = int _(0)^(oo)(dx)/((x^(2)+ 4 )(x^(2) +9))`
` = 1/5(int _(0)^(oo) 1/((x^(2)+4)) dx - int _(0)^(oo) 1/((x^(2)+9)) dx )` ,
` = 1/5 [ [ 1/2 tan^(-1). x/2 ]_(0)^(oo) - [1/3 tan^(-1) x/3 ]_(0)^(oo) ]`
` = 1/5 [ (1/2 .pi/2 -0) - (1/3 . pi/2 -0 )] = 1/5 (pi/4 - pi/6) = pi/60`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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