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What is the integration of log(sinx+cosx) from -pi/4 to pi/4 ?

What is the integration of  log(sinx+cosx) from -pi/4 to pi/4 ?

Grade:12

1 Answers

Arun
25750 Points
5 years ago
512-2383_59.pngNow refer to the following steps to solve for the simplified integralI =1/2\int \limits_{0}^{\pi/2}log(cost)dtNow put 2x = t which implies, dx = dt/2I =\int \limits_{0}^{\pi/4}log(cos2x)dx2I = \int \limits_{-\pi/4}^{\pi/4}log(-sin^2x+cos^2x)dx = \int \limits_{-\pi/4}^{\pi/4}log(cos2x)dx = 2\int \limits_{0}^{\pi/4}log(cos2x)dxI = \int \limits_{-\pi/4}^{\pi/4}log(sinx+cosx)dx = \int \limits_{-\pi/4}^{\pi/4}log(-sinx+cosx)dxThis is a tricky questionFirst put x = -x and add
 
 
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Arun (askIITians forum expert)

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