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OpenStudy (anonymous):

how do I integrate f(x)=(x.cos^2(x))/2 ?

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myininaya (myininaya):

You will need to use \[\cos^2(x)=\frac{1}{2}(1+\cos(2x))\] and integration by parts.

myininaya (myininaya):

\[\int\limits_{}^{}\frac{1}{2}x \cos^2(x) dx=\frac{1}{2}[(x) \cdot (\frac{1}{2}(x+\frac{1}{2}\sin(2x)))-\int\limits_{}^{}(1) \cdot (\frac{1}{2}(x+\frac{1}{2}\sin(2x))) dx]\]

myininaya (myininaya):

I used (x)'=1 and int(1/2*(1+cos(2x)))=1/2 *(x+1/2*sin(2x))

OpenStudy (anonymous):

thanks

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