Although it is often true that a double integral can be evaluated by using either $d x$ or $d y$ first, sometimes one choice over the other makes the work easier. Evaluate the double integrals in Exercises 37 and 38 in the easiest way possible.

$\iint_{R} 2 x^{3} e^{x^{2} y} d x d y ; \quad 0 \leq x \leq 1,0 \leq y \leq 1$

## Discussion

## Video Transcript

so we would like it to me for a way to distribute Figel form this boners way. We have eggs. There was a little poor x times way dx dy way zero x is from zero toe to any wise from 0 to 1. Your silverware. The good defense is ust Miller. Just that give our weights to integrate with respect. Oh, all right, cause incident. We know dysfunction. So there's gonna be equal to integrating for a story with respect to wash. Have zero toe too for your fixer here. Then you have very office The room to war on a very avoid here exam and it's a bore. Exam time. See why d y the decks room there Where? When we have exponent and tried to rights form You're here if you have. If we have Frank our friendship Ito bore a functional for ex Did say you off X and a girl 50 with respect to X. This is good too. Ito bore you off. Begs over you off eggs. Very evocative. So we have the same thing here, have people ex then dividing by ex. We gave this one so there's gonna be a good too here. This is good through any group Zero, 22 And we can integrate immediate three and cigar off. This one is that Sable This world with respect to why? If we was dis mattered This is good too. Be to bore eggs. Why? Because we have to eat before I go to this one dividing by right? Because you know, you remember that the X's constant means that we have no dysfunction. It's questions off. Why, sir, we have Ito bore eggs. Why? Over the vertical from extremes. Why you've respecto white Mr X so X over eggs is going to want So we carve this very you. Then we have our waited from zero No, from 0 to 1. Yes. Then the ex So far so good. This is good too. This kind of being good too Three put exclude toe. Why couldn't one here we have a little bar. Eggs is that is a sugar form a 0 to 2 Tito boa one When you put zero this good to zero it was zero is goingto one. So we have these the awful pigs. So this is, um, his Christian. Excuse him. If we put I quit toe one with hers here. Eggs? Not one, because we have X time was one. But if we put zero, we have X times zero is zero. So is one. So this is good too. You remember that ticked aggression off X is X over Xterra. Relative scotch. One means that his ex and rich ex. This is different addict property minus integral for one is X. So it didn't report the brokers here, which is going toe to toe zero. This is good too. It abroad too minus two. They remind us it's a boy. Zero is one. They d minus zero, but minus and manners dispersed. Impresses even which is good, too. Into board too minus one. Is it a board to minus one? Then the answer. Well, sorry, because this is minus y. This is the one made another mystic here. Just Yes, this is press, but this is minus because it's minus each Brazil. It's minus one. So here is that the minus three Feuz or great gets up, We can have fool point three age nine. Good to wear zero five. So unit, Because here they mean it as very young. This is Wendy Group. The Fairy of Dysentery Group is for 0.389

## Recommended Questions