Give an example of a region that cannot be expressed by either of the forms shown in Figure 34. (One example is the disk with a hole in the middle between the graphs of $x^{2}+y^{2}=1$ and $x^{2}+y^{2}=2$ in Figure $10 . )$

The idea of the average value of a function, discussed earlier for functions of the form $y=f(x)$ , can be extended to functions of more than one independent variable. For a function $z=f(x, y)$ ,

the average value of $f$ over a region $R$ is defined as

$\frac{1}{A} \iint_{R} f(x, y) d x d y$

where $A$ is the area of the region $R .$ Find the average value foreach function over the regions $R$ having the given boundaries.

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## Video Transcript

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Why is the local so 20 minus one when executed zero whites go to zero when Wise could execute toe one wise goto one when wise when execute too two. Then why is go to two? No, Sorry. It's good to her. One over two because one over x. So this could talk. One about which is goingto 25. Good. So and very ill for X. There's untouched function. Which school? Executed to assist. Other question. So it's right to sketch this kind off function. Just get this burners and find that way. Are the boners off her, Huh? Here we have that. We kind of have one. Yeah, we can have to donate. To draw so many points is just to see Wayne. Um, the Here we have minus one and remind us too. They were gonna have a while. Here. We're gonna have to. This is a why this is the X saying sexiest, this door. Exit 12 Okay, this is here. We have minus one and minus two. So let's delight to skip the first function. We can sketch because excess kowtow to This is the type of function this one become show. 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Interviewer of Aaron to wear enough to his constant Mister, Just take off the eggs which is goingto eggs that we heard of two minute that we have to Aaron off two times x But except for wait too 1 to 2. You sit too. So this is good too. If we put very affects here is 22 minus one is one So it's going toe rogard team off too If you'll excuse You're very crater You can find the final for you which is good too One points three fades six two mine sword You see the answer for a Popara?

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