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Evaluate : ∫30 dx/(9+x2) - Mathematics

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Evaluate : `int_0^3dx/(9+x^2)`

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Solution

Given,

`I=int_0^3dx/(9+x^2)=int_0^3dx/(3^2+x^2)`

We know that, `intdx/(x^2+a^2)=1/atan^(-1)(x/a)+C`

Therefore,

`I=int_0^3dx/(x^2+3^2)`

`=1/3[tan^(-1)(x/3)]_0^3`

`=1/3[tan^(-1)1-tan^(-1)0]`

`=1/3[pi/4-0]`

`=pi/12`

 

Concept: Evaluation of Simple Integrals of the Following Types and Problems
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