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Numerade Educator

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Problem 64 Hard Difficulty

$f(x, y)=e^{2 x+y} ; \quad 1 \leq x \leq 2,2 \leq y \leq 3$

Answer

$\frac{e^{7}-e^{6}-e^{5}+e^{4}}{2}$

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Video Transcript

Okay. Another average valley of this function. He too. The two x plus y Thanks. On the rectangle. One to cross two, three. Well, they're This rectangle is just a rectangle is actually a square The side length one So the area is just one So the average value is going to be one over a But that's just one. So we don't even need to write that. So it really is just going to be equal to the value of the integral which Okay, so I guess we'LL do y first too. Two, three, one, two. Of course. Doesn't matter. Needed the two backs. Plus, why don't we have tea? Why? Ex? Okay, one two anti derivative is just itself to explicitly by that, I made it from two to three. So then, yeah. One two, Meet Teo to x, of course. Three minus b to the A to X us too. We take an anti derivative that both these will get a factor. One half and then just themselves. Six plus three minus needed. The two x plus two I read from one to. So you get one half and then good plugging to get a t The seven minus eight six, and then plug in one. It's E T B by in the minus minus plus mmm to the fore.