00:01
We want to evaluate this double integral over the region x between negative 1 and 1 and 1, and y between 0 and pi.
00:10
Now, since our region here is just rectangular, and we have nothing where our integral will depend on the other variable, we can go ahead and apply essentially fubini's theorem, and it says it doesn't matter in which order we integrate.
00:30
This.
00:32
So i'm just going to write this as the integral from 0 to pi, negative 1 to 1.
00:38
So this outer integral is y, the inner 1 is x, and then we have xy, cosine, y, dx, d, y.
00:50
Now remember the way we read this is we integrate this inside integral with respect to x, and we assume y is a constant.
00:58
Well, if y is a constant, let's go ahead and factor that out.
01:00
So we're going to have the integral from 0 to pi of y times cosine y times integral from negative 1 to 1 of x d x d y...