00:01
All right, so here is an iterated integral, and we've got an integral from 0 to 1 of the integral of 0 to 1 of the quantity x plus 1 y squared, dx, y.
00:13
Okay, so the way that i like to do these integrals, instead of having to do a u substitution, let's actually foil this integrand out.
00:23
Okay, so when we foil this integrand out, we're going to get 2x squared, i'm sorry, we're going to get x squared plus 2xy plus y squared.
00:37
Dx, d .y.
00:40
All right, so now this first integral here, i'll underline it, or i'll circle it in red, is the inner integral, as i like to call it.
00:50
And we're gonna integrate this with respects to x.
00:52
Okay, so everything that does not have an x in it is not considered a variable, but a constant.
00:58
So this first one here, x squared integrates just as usual, plus this 2x, y, this y, is a considered a constant times the integral of 2x is x squared and over here we've got plus y squared which is a constant and we integrate a constant we get y squared x we're going to evaluate this guy from zero to one and then we're going to take the the integral of that again so when we plug in one we're going to get one -third plus y plus y squared and when we plug in zero, we're going to get zero for each one of these three terms...