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Problem 46 Easy Difficulty

Evaluate each double integral.
$$
\int_{0}^{1} \int_{2 x}^{4 x} e^{x+y} d y d x
$$

Answer

$\approx 23.1208$

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Video Transcript

{'transcript': "Alright, here we have this double inter girl So euro to one two x four x of Okay, you do the X plus y Do I dicks, Okay. Anti derivative of e to the X plus y. It's just itself. So that's if we want to go ahead and evaluate Uh, so we just have each of the express y evaluate at four X So that's going to be easy to the five x minus e to the three x The thanks. Mhm. All right. And then so we just evaluate where we take an anti derivative. So we get E to the five X over five minus e to the three X over three, evaluated from 0 to 1. Well, this is just eat of the 5/5 minus e cubed over three and then minus. We need to evaluate these zero. So that's going to give me a plus one third and I'm minus 1/5. Well, one third, minus 1/5. So this is 15. A 5/15 minus three of her 15 to 215. So you do the five over five minus E to the 3/3 plus two over Team"}