How do you find the integral of #f(x)=sin^2x# using integration by parts?

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Answer 1 · 2016-07-08T19:39:47

You have to use the half angle identities to evaluate the indefinite integral.

Let #sin^2(x) = (1-cos(2x))/(2)#, then

#int sin^2(x) dx #

#= 1/2 int 1-cos(2x) dx #

and by letting #u=2x#, so # du = 2 dx -> 1/2 du = dx#

Thus

#1/2 int 1-cos(2x) dx #

#= 1/2 x - 1/4 sin(2x) + C#

#= 1/2 (x-1/2 sin(2x)) + C#

For this problem, it is best to use the half angle identities rather than integration by parts.