Evaluate the definite integral.?

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1 Answer
Apr 24, 2018

0

Explanation:

This can be solved using the following substitution:

u=x^2

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

Lower: u=0^2=0

Upper: u=(sqrtpi)^2=pi

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:

1/2du=xdx

And we get

1/2int_0^picosudu=1/2(sinu|_0^pi)

=1/2(sinpi-sin0)=1/2(0-0)=0