Evaluate the definite integral.?

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1 Answer
Apr 24, 2018

0

Explanation:

This can be solved using the following substitution:

u=x2

Since this is a definite, calculate the new lower and upper bounds using the substitution:

Lower: u=02=0

Upper: u=(π)2=π

Take the differential:

du=2xdx

We see that xdx is present in the integral. As a result, we can divide both sides of the differential by 2:

12du=xdx

And we get

12π0cosudu=12(sinuπ0)

=12(sinπsin0)=12(00)=0