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# Evaluate : ∫30 dx/(9+x2) - CBSE (Science) Class 12 - Mathematics

ConceptEvaluation of Simple Integrals of the Following Types and Problems

#### Question

Evaluate : int_0^3dx/(9+x^2)

#### 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

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#### APPEARS IN

Solution Evaluate : ∫30 dx/(9+x2) Concept: Evaluation of Simple Integrals of the Following Types and Problems.
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