00:01
We're given an integrated integral and we're asked to evaluate it.
00:06
The iterated integral is integral from 0 to the square root of pi, integral from 0 to x, integral from 0 to x, of x squared sine y, d, y, d, d z, d x.
00:36
To evaluate, first we'll take the antiderivative with respect to y.
00:42
So we get integral from 0 to the square root of pi integral from 0 to x of negative x squared, cosine of y from 0 to x, d z, dx.
01:08
Simplifying, this is integral from 0 to 0 to x, and then substituting in for y, this is negative x squared well, times cosine of x and then minus negative x squared, which is just positive x squared.
01:42
So we have x squared minus x squared cosine x, d x after simplification...