1. The problem statement, all variables and given/known data Hey guys, so we're going over multiple integration in Calc III, and I'm having trouble with the more complex problems. ∬ √(x + 4y) dxdy, where R = [0, 1] x [2, 3] So it's 0 to 1 on the outside integral, 2 to 3 on the inside integral, of sqrt(x+4y) dxdy. 2. Relevant equations Iterated Integrals u-substitution 3. The attempt at a solution I solved the previous double integration problem, but using u-substitution in two variables is throwing me off. I would assume that, u = x + 4y du = 1 dx (since we're integrating with respect to x first, and holding y as a constant, so x becomes 1 and 4y drops out). So du = dx = ∬ √(u) du = ∫(0 to 1) [(2u^(3/2))/3] (2 to 3) dy = ∫(0 to 1) (((2(3 + 4y)^(3/2))/3) - (2(2 + 4y)^(3/2))/3)) dy And this is where I stopped since this seems way overly complicated, and I feel like I did something wrong. My main problem: Change of variables: If I want to change the integral variables, i.e. 2 to 3, I know in the single variable case that you use the u equation. But here, u = x + 4y, it has two variables. I only have 2 and 3 so do I just plug that into the x and completely ignore anything attached to a y? Pretend the y isn't there? It doesn't make much sense to me. u-substitution in general, with multiple integration: I'm not sure if I'm going through the process after that correctly, either. If I could figure this out, and know the correct way to do these kinds of problems in general, I could do much more, but for now I'm stuck on all of these problems since they're mostly similar. Thank you very much for any help or input!