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What is the average value of over the square?The average value (Type an exact answer )What is the average value of over the quarter circle?The average value (Type a...

Question

What is the average value of over the square?The average value (Type an exact answer )What is the average value of over the quarter circle?The average value (Type an exact answer )

What is the average value of over the square? The average value (Type an exact answer ) What is the average value of over the quarter circle? The average value (Type an exact answer )



Answers

Calculate the average value of the $x$ -coordinate of a point on the semicircle $x^{2}+y^{2} \leq R^{2}, x \geq 0 .$ What is the average value of the $y-$ coordinate?

So far from for the and we have to find the average value of one over R squared over the given annual IHS. So let's set up our polar double integral. So this is an annual list. The fate of balance are going to be from zero toe pie, and the are bounds are given to us there from 2 to 4 and the function is one over r squared. And since this is a polar double, integral, don't forget to multiply the entire into grand if I are and then the r and D Fada and we can go ahead and start integrating. So I'm just gonna split apart the insert the inter girls, the double integral. Here it's so it's going to be the integral from 0 to 2 pi beta Multiply that by the integral from suits or four of one over r g r. And remember, you can only do this if all of the bouncer constants. So if we integrate, we're just gonna get to fly on the left and Ellen of our on the rights. And from here the four. So if a plug in values really Jessica Ellen of four minus Ellen of two. And if we combined them using a longer property, we would just get Ellen of to And then we multiply the results from both sides together. So it's gonna be to find el enough And now to find the average value U divided this result by the area of the annual IHS. So the area of the annual IHS isn't literally just the same ends a girl from zero to fire from here before and the Instagram it's just gonna be R and D are indeed data, So we're gonna have too high times. If you're integrated with a dress again, 1/2 times are SKoreans from two before I'm gonna fact, are there one paths that's gonna be 1/2 times 16 minus four or just sex, multiply them together, gets for fine, and then we're going to divide to find times Ellen of to by 12 times. And if we do that applies, cancel out and we would just end up list l enough to over six and yeah, that's basically young

Into question here will record a distant which in the pond X y Judah arches are zero. There we go to the X squared plus y squared and the square in a distance here and the fall first Want to compare the deeper into grow off the X squared plus y square G. I, uh well hello, ricin. On coaching the X quiet when x is between the minister to chew on wise between the search to and and for once you get equal to we can turn this image of that double integral X squared plus quite square. And now And we put it the wife, us and the X after. So why does from them jokey to an extent from honest you choose to Then we get Nico Jew. But you know we have Why would be the variable? Therefore we have the months to chew And why would be variable x will be the constant so entire every day with your ex quantum skwy press Where about 303 Even though I didn't deserted to G thanks Then we get in co two months to to do so, we Will it do inside Gundha Teoh X square plus na to be a 803. And now the X Yeah, notice Standard function in sign is that even function their phone can Teligent into the Jew attempts in the government that you two now geo X squared plus eight with three t x get injured at you And now here we get the entirety of the culture that Ah, thanks, Bela Tree of ah, three times to here. Plus I ate at the three. Thanks. He violated under 30 Do so we had included it too. And we would it to in some wonder job Uh 38 And teams will be 16 out of the three. Plus, there were also equals 1603 and the phone Get Nico to the 32 sixty four hundred three. And now this ricin Here we have the area. You go to hell a distant Haygood, Your phone on a distant Could you do never? We have four times to originate and found the average value we go, Jew. The sixty four hundred three developed by eight. Then we get Nico to the eight at a three

In this problem we have to describe. There were its value of the function in our own word for that. So let's if he's a function from e commerce, be close, interfere toe are on dhe. If it's continuous, then the average for do off. If this stuff we off the rectangle, Who's Lynn? Oh, one site B minus C And who's video is equals to the idea underneath the guard? Why is he going to be here for a fix between the close interval? A comma p. So let's try to justify it that it indeed in capsule it the exact notion off every its value of the function. Uh, the idea under the guard, Why you sick? Oh dear. For a fix in the closest interval, E Coma B is given by the definitive krill from you to be if all fixed e x no, that a temple, we'll have the length. Is it going to be my nest on? The wit should be called to the emperor. Its value of the function there's called the quantity is O R. Average do all fifth. So then this In place E, it's 1/4 to one divided by B minus C Integration from A to B before fix D X. And now this guy does agree our usual definition off efforts. Can you affix?

In this question were asked to compare the average value over a square and over 1/4 circle. Still, we're gonna compete oil, compute these two values respectively, and compared them to see which is larger. So for the square, simply from 0 to 10 to one with an accident. Why? With about to be this is one this one. So the first value is zero ones with once. Why the 60 y and this you battle, it's two on. So first, we we've Alice this in the park, which is rich in ads, and we're gonna end It was half. What do you want from 0 to 1 so well, which is 1/4 that's for the square. And for the average value over 1/4 circle. Where you gonna have first? We're gonna divided by the area of a circle because quarter circle has area pie tons. Ours one escort over four kisses quarter. So that's the area of the circle here. And, uh, the ends. A girl is going to be 1 4 0 to 10 to score with one squared X. What the what the X, Because the diagram for it the region is revel in is this the outer circle? And we voted this integral. Let's see, we have two over pie on Syria to one x minus as Cuba, the S O. That was one over to pie. And, uh, this is roughly, let's see, the capital leader on roughly 0.16 And this is their one too far. So apparently this is larger, so swear has a larger average value.


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