HSC Arts 12th Board ExamMaharashtra State Board
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Evaluate: int_(-a)^asqrt((a-x)/(a+x)) dx - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

Evaluate: `int_(-a)^asqrt((a-x)/(a+x)) dx`

Solution

`int_(-a)^asqrt((a-x)/(a+x)) dx`

Let `I=int_(-a)^asqrt((a-x)/(a+x)) dx`

`=int_(-a)^asqrt(((a-x)(a-x))/((a+x)(a-x))) dx`

`=int_(-a)^a (a-x)/sqrt(a^2-x^2) dx`

`=int_(-a)^a a/sqrt(a^2-x^2) dx-int_(-a)^a x/sqrt(a^2-x^2) dx`

[but `a/sqrt(a^2-x^2)` is an is an even function and `x/sqrt(a^2-x^2)` is an odd function]

`=2a.[sin^-1(x/a)]_0^a`

`=2a.[sin^-1 1-sin^-1 0]`

`=2a[pi/2-0]`

`int_(-a)^asqrt((a-x)/(a+x)).dx=pia`

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APPEARS IN

 2016-2017 (March) (with solutions)
Question 5.2.3 | 4.00 marks
Solution Evaluate: int_(-a)^asqrt((a-x)/(a+x)) dx Concept: Properties of Definite Integrals.
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