HSC Science (General) 12th Board ExamMaharashtra State Board
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# Solution - Evaluate : ∫π0 x/(a^2cos^2 x+b^2 sin^2 x)dx - HSC Science (General) 12th Board Exam - Mathematics and Statistics

ConceptMethods of Integration - Integration by Substitution

#### Question

Evaluate : int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx

#### Solution

I=int_0^pix/(a^2cos^2x+b^2sin^2x)dx.............(i)

I=int_0^pi(pi-x)/(a^2cos^2(pi-x)+b^2sin^2(pi-x))dx

I=int_0^pi(pi-x)/(a^2cos^2x+b^2sin^2x)dx...........(ii)

Adding (i) and (ii), we get

2I=int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx+int_0^pi(pi-x)/(a^2cos^2x+b^2sin^2x)dx

2I=int_0^pi(pi)/(a^2cos^2x+b^2sin^2x)dx

I=pi/2int_0^pi1/(a^2cos^2x+b^2sin^2x)dx

I=pi/2int_0^pisec^2x/(a^2+b^2tan^2x) dx (dividing numerator and denominator by cos2 x)

Substitute tanx=t ⇒ sec2xdx=dt

t=tanx=0 " at " x=0 ,t=tanx =0

I=pi/2int_0^0dt/(a^2+b^2t^2)=0

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#### APPEARS IN

2015-2016 (March) (with solutions)
Question 5.1.3 | 3 marks

#### Reference Material

Solution for question: Evaluate : ∫π0 x/(a^2cos^2 x+b^2 sin^2 x)dx concept: Methods of Integration - Integration by Substitution. For the courses HSC Science (General) , HSC Science (Computer Science), HSC Science (Electronics), HSC Arts
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