Enroll in one of our FREE online STEM bootcamps. Join today and start acing your classes!View Bootcamps

Problem 34

Find the volume under the given surface $z=f(x, y…

04:53
Problem 33

Find the volume under the given surface $z=f(x, y)$ and above the rectangle with the given boundaries.
$$z=x \sqrt{x^{2}+y} ; \quad 0 \leq x \leq 1,0 \leq y \leq 1$$

Answer

$\frac{2}{15}\left(2^{5 / 2}-2\right)$ cubic units.



Discussion

You must be signed in to discuss.

Video Transcript

So we're going to find a very, um, off dysfunction dysfunction reaches goto X squared off excess square press. Why way a zero is the list and I go to wash this down and go to one. And cee lo list honor, go to X Reston. You go to one. It's that very off Rex. And very off. Why are between zero in decorum? This is Ranger fakes. Anyway. So to find a very you, it's our very This is good too. We can't have the insignia from zero toe one. See? Very awful. Why? And I grow from 0 to 1 off x This for Frank's. We can read this square root as exist. Cleared. Press away four through poor one over two. Then the eggs their way. Good. So we can let, um, this for you exist. Rare press. Why, which is equal to thi this way Gonna be good. Have take equal to excess. Crea changes. Very. Bruce, if you have tea, which is good too exists Clear. Press wide in the discus. Do you off eggs? The off white day off t. It's good to free. Depreciate this. Goodbye X here, buddy. We have to exit did you? And there's a very of tea. Can a peak too. They range of tea when exclude to zero. He is good toe watch. When very off exits Goto one to really be a good tool. Why press one sore on tickle or wearing? We'll be good too. Sorry. And the groom from zero toe one. Then take her from here. So why Yeah, Why press one the square. So I press one. This is a very off t so x wing, because here we have exit e x, you can have the exit d X is good toe DT off to such. We can have a one off to here. Then we have tea. Have tea to bore one over two. Don't be computer confused. Here is not a negative is just one we're not going to Yeah. Then did you? It's too, too poor or in over two the city to pour run over to right. It's a good way if so, are very in free beacon too integral from 0 to 1 is that we are going to integrate. This one misstep is because we have to two per one off a to remember that we have to add the one and divide that's number. So we we have tea. I mean, but that's we have one over to here. Then here we have tea to Bower. One of the two press. Well, is three three over two over three. All right. Too struggling, too. Then we pulled you. Very you. Why press one and why? Tentative. Great. With respect to why good? This is country in sugar from 0 to 1. So here is one of our three over two is to over three witches. Goto was one over to this one of us three on bread this year. This is good too. Three. Here. You see one good. So we're going to put this where you wash. This is a wash. Press one. Bora, You over too. Minus. Put this very here with ever Y two bro. Three over too. Then another practice, then deep. Why? So we're going to integrate with respect to work, can trade this watch and then threw it to this one. This is good too. One of us. See? Here we have three over to press one over to please press one is a five over to some things that the Y press one toe boa five over too. But dividing five over too. Very well minus. Why Turbo? A five over too. Over by Over too. Then devour you. It is 01 So far so good. Justice good too Can have to over 15 because I have to refrain two over 15. Then we're going to put their very four here. This one plus one is to to power five over too. Minus zero. Press Juan, this is minus one minus. This is one Sue one minus zero. This is Sarah. So it's two per five over to minus two. Throw from 15. Which is good too. It's gonna be good too. Another 15 here is minus two. Is minus four a nest for then impress two too poor for two times. He this is forward means eight squared off too. 80 square root of two. This is good too. Fine. If you can create this with your cricketer is good too. 0 48 minus four plus eight. Square root of two over 15. Which is good too. 0 48 little 0.40 It Ah, 75. And so unit off Valium. So this is the answer. It's minus full press. Aide scared it off to over 15 unit proof brain is very, um, we're asking you to carry great.