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Evaluate : int0^oo1/(a^2+b^2x^2)dx...

Evaluate : `int_0^oo1/(a^2+b^2x^2)dx`

Text Solution

Verified by Experts

I= `int_0^oo1/(a^2+b^2x^2)dx`
I=`int_0^oo1/(a^2+(bx)^2)dx`
let bx=t
or dt=bdx
I=`1/bint_0^oo1/(a^2+t^2)dx`
I=`1/b(1/a)(tan^(-1)(x/a))_0^oo`
I=`1/(ab)(pi/2)`
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