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Problem 52 Hard Difficulty

Use the region $R$ with the indicated boundaries to evaluate each double integral.
$$\iint_{R}\left(x^{2}-y\right) d y d x ;-1 \leq x \leq 1,-x^{2} \leq y \leq x^{2}$$




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Video Transcript

Okay, here we have the double inner girl minus one toe, one minus x squared. The X squared of X squared minus. Why, T o P X. Starting with an anti derivative. With respect, sir. Why? Since it's going to be X squared? Why? Minus y squared Cover two Evaluated Trump X squared Tio X squared. Okay, so something nice happens here. This is this term is going to give me zero, because it's going to be OK, x to the fourth minus, thanks to the fourth. So she's here, so that's great. So I only have this first term, and this is going to be X squared times just X squared, minus minus, x squared the ex, which I mean, what is this? That should just be X squared. Times to x squared, too. Next to the fourth. Okay. Okay. So we need inside. Riveted to X to the fourth. Well, that's gonna be too x to the fifth. Evaluated for Maria's fall into one that's going to be two fifths times one minus minus one. Just to serve for but

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