00:01
So we're asked to evaluate the following double integral over the region r.
00:05
So we have the double integral over r of x plus 6y, da, where r is the point xy for x ranging from 1 to 4 and y ranging from 2 to 4.
00:19
So it's important to know that da is shorthand for the change in area, which is going to be our dx, dy.
00:31
So when we rewrite this integral in terms of the region r, we will do it.
00:39
We'll put our integration limits based on dx and d .y.
00:44
So we'll have the integral from 2 to 4, the integral from 1 to 4 of x plus 6y, and then we'll have dx, dy.
00:54
It's important to note that this integral, whatever variable this is, dx should match.
01:03
The integration limits that were given to us, and then the outside integral, d .y will match the outside integral limits...