00:01
For this problem, we are asked to sketch the region of the integration for the iterated integral from 0 to 2 of the integral from x to 2 of each power of negative y squared, d .y, d .y, d .x.
00:12
Then to evaluate the iterated integral where it will be necessary to switch the order of integration.
00:19
So to begin, we can see that just by reading off from the integral, we have that x will be between 0 and 2, and we have that y will be between x and 2.
00:29
So our region of integration, let me sort of sketch this out here, put x equals 1 there, so x equals 2 is here, and we have that y is going to be between 0, or not 0 necessarily, though it will be when x is 0, up to 2.
00:47
So our region of our region, i should say, of integration will be the upper portion of this region shown here, so it will be r as shown there.
00:58
Now we can note that to switch the order of integration, we'd want to imagine drawing a horizontal line across.
01:06
We can see that we first intersect the line at x equals zero, then we intersect the line at y equals x or alternatively at x equals y...