HSC Arts 12th Board ExamMaharashtra State Board
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# If ∫a0 1/(4+x2)dx=π/8 , find the value of a. - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptEvaluation of Definite Integrals by Substitution

#### Question

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

#### 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

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Solution If ∫a0 1/(4+x2)dx=π/8 , find the value of a. Concept: Evaluation of Definite Integrals by Substitution.
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