Grade 12Trigonometry

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

Sai Soumya

8 Years agoGrade 12

1 Answer

Arun

8 Years ago

Now refer to the following steps to solve for the simplified integral $I =1/2\int \limits_{0}^{\pi/2}log(cost)dt$ Now put 2x = t which implies, dx = dt/2 $I =\int \limits_{0}^{\pi/4}log(cos2x)dx$ $2I = \int \limits_{-\pi/4}^{\pi/4}log(-sin^2x+cos^2x)dx = \int \limits_{-\pi/4}^{\pi/4}log(cos2x)dx = 2\int \limits_{0}^{\pi/4}log(cos2x)dx$ $I = \int \limits_{-\pi/4}^{\pi/4}log(sinx+cosx)dx = \int \limits_{-\pi/4}^{\pi/4}log(-sinx+cosx)dx$ This is a tricky questionFirst put x = -x and add

Regards

Arun (askIITians forum expert)