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Draw the appropriate figure.Repeat Exercise 31 for the integral $$\int_{1}^{2} \int_{0}^{2-y} \sqrt{1+x^{2}+y^{2}} d x d y$$

Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 4

Double Integrals

Partial Derivatives

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like this to before we evaluate the integral exactly as it's written. They would like this to sketch the region. We're evaluating our continuous function. That's two of X over. So it seems a region those curves the quiet because they're gonna Lipson because we have an X squared over four is equal to one minus y square. We could add that to the other side. Yeah, it's an ellipse, and that's over for us. Maybe to his over here. Um, it's with respect of wines of X. So that's Ellipse Region and revere comic sections. Throw any day on linear algebra? Um, let's see. Well, why will be from zero the one? It's, ah, virtually that handbrake. It introduced the top half. They broke it into this half and this half, but that's what they want us to work with. So we'll do it buzz instead, from zero, the one the only want us to evaluate up to year. Yeah, that corresponds with, uh, let's see over B squared over one square. Yeah, that only wondering. So let's see. That's evaluated. Okay, 01 let's see. X squared. Evaluated to square one minus sliced bread and negative two square root of one minus y squared the line. But I think you see what's going. We're going Teoh, evaluate, and we're going to get for times the square root of one on this. I swear I'm really not subtract. Let's see the night if she goes away for some scared of one minus y squared. Now we have a number and our quantity and it's additive inverse, so we just have zero on the inside with zero integrate.

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