Ex 7.11, 10 - Evaluate (2 log sin x - log sin 2x) dx - Ex 7.11

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  1. Chapter 7 Class 12 Integrals
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Transcript

Ex 7.11, 10 By using the properties of definite integrals, evaluate the integrals : 0 2 2 log sin log sin 2 Let I1= 0 2 2 log sin log sin 2 I1= 0 2 2 log sin 2 sin cos I1= 0 2 2 log sin log 2 log sin log cos I1= 0 2 log sin 2 log cos I1= 0 2 log sin 0 2 log 2 0 2 log cos Solving I2 I2= 0 2 log cos I2= 0 2 log 2 I2= 0 2 log sin Put the value of I2 in (1) i.e. I1 I1= 0 2 log sin 0 2 log 2 0 2 log cos I1= 0 2 log sin 0 2 log 2 0 2 log sin I1= 0 2 log 2 I1= log 2 0 2 I1= log 2 0 2 I1= log 2 2 0 I1= log 2 1 2 I1= 2 log 1 2

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