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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