If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.

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#### Solution

given that `int_0^a1/(4+x^2)dx=pi/8`

We need to find the value of a.

`Let I=int_0^a1/(4+x^2)dx=pi/8`

`Thus,I=1/2(tan^(-1)(x/2))_0^a=pi/8`

`=>1/2 tan^(-1)(a/2)=pi/8`

`=>tan^(-1)(a/2)=pi/4`

`=>a/2=tan(pi/4)`

`=>a/2=1`

`a=2`

Concept: Evaluation of Definite Integrals by Substitution

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