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Problem 29

Find the volume under the given surface $z=f(x, y)$ and above the rectangle with the given boundaries.

$$6 x+4 y+7 ;-3 \leq x \leq 3,2 \leq y \leq 4$$

Answer

54 cubic units

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## Discussion

## Video Transcript

So two friends at variance with the problem today is just to find the very fraction were given this function. Um uh, this strange off don't mean a fraction So there's a formula to find their value. If we have a function, you see, say Z, which is go to, for example, function off tool Very use Ables X and why? Well, you know we can have this can't be the vertical or it's gonna be access so that if we have a very off the demon off X is maybe a It won't be this done or go to eggs is then they go to big and why maybe see place Then I go to why and then I go to Dame in discuss they're for you. It is good too. Integrating from baby a toe being on limited Great from 62 a day if fo for eggs if off ex away where it's there, the why and the X So that's our Christian. Our problem now is very easy because we have. If we're ever function here, I don't know if re writes to function very well here. There's a wife. Thanks. And why? Because you have two very risk here. Um, so this is like here on this, Like, here. Is that our function? Our Brian we beaker too. M a group from boundaries or four eggs is minus 3 to 3. And then until you go under, is before I there 2 to 4. They're no function questions. 60 eggs for us Seven. Why? Pros seven. Then do you weigh Banded DX? Good. So far, so good. Do this. Give us the very, very, um is good too. And they grew from minus three, two, three. We can never went to descend. Circle respect toward the white bits that we have six x y Here you have six, six eggs times. Why press? This is seven and take her off. Why? Which is good toe seven over too. Why scream? Why scream press and to really eating seven with respect a wise a seven way Then the he everybody very full full. Why, Devery? For why Two and four? Yeah. Two. Then d x be ex good. This volume is good too. Kensico minus three, two or three off If we push for Here is 24 x 24 eggs minus toe work X you see three ports for here 24 times 6 to 24 minus two times six times manners Where so is toe. Where the been read one very where this is theworld eggs because probably very awful white heat. So here we have France crayon 16 minus to scare is to wear So twere if over two years six Dear Suzy Fourty two, then press you have very ifwe So is the full minus two is too. This is full. So is 56 the awful eggs 42 press 14 is 52. This can't be Goto 52 56 priests. Sorry. So, uh, this is sculpture integral off 12 express 50 c x, which is good too. The food's great here eggs. This is excess grayer over to which is sexy eggs created presi 50 60 eggs and then we ever put their value minus 3 to 3. Good. So far so good. And this is good too. If you put three here with her nine miners who put three here is nine again. This is got to zero goes negative for us people. He, uh, three three miles ministry is plus three. This is six So this is good too. 56 times it six, Which is going to mystify. Did it make you a mystic? Here, Choose. Uh, very off right here. This is full. So full time of six is 24 minus one Terrorist. Where the X this is correct. He, uh this is that square 16 minus four is to wear it toe. Where is ah for over 2 16 is the 66 times seven, for truth is correct. So this is for minors to is for times. Two times seven is 40. So 56 are nice. So then the answer. Get him down, sir, They'll say six. 56. 56. Time of six. This is a touch of six 336. This is there, sir. I'm not sure. Fred Image, Mr. Just see, that's not China soon, but the procedure and the sister procedure be if there's a mistake on computation, have to take away this. They ask, Don't worry. Thank you very much.

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