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anonymous
 one year ago
Volume of a graph (Washer)
anonymous
 one year ago
Volume of a graph (Washer)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Find the volume of \[y=\sqrt{x}\] about x=4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I started with \[x=y^2\] so would that be the outer radius?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441595115874:dwroughly

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3x=y² is not the same as y=√x because it will have a twice larger volume

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry I forgot to mention it is bounded by y=0 so just quadrant 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3oh, and then if it is rotated about x=4, then I will assume that this is where the √x region ends at?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Oh, ok, so you know that your limits of integration are from 0 to 2. \(\large\color{black}{ \displaystyle \int_{0}^{2} \pi\left(y^2\right)dy }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So, you can tell that your radius is y², and it is from y=0 to y=2. THis is what I would do.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I missed it should e y^4

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3\(\large\color{black}{ \displaystyle \int_{0}^{2} \pi\left(y^2\right)^2dy }\) because radius squared. Sorry

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3So that is just an integral of \(\pi\)y\(^4\) from y=0 to y=2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow I tried this the first time and I guess I integrated incorrectly so I was so confused!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3you can put integral into wolfram. what is important is to get a good practice of making a setup of the integral for volume. integration you know already....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.332π/5 is what i got. (want to know how to make a π • ÷ × √ with no latex?)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0here are some probs with the solns, pg3 has a nice little summary

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That will definitely be useful, thank you

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I am glitching a bit

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Ok, so here is going to be a short guide. The algorithm is: \(1)\) Click ALT and hold it \(2)\) Click the "Number Code" (on the numberpad on the right of the keyboard if you got one) \(3)\) Release the ALT  Number code Result 0, 2, 1, 5 × 2, 5, 1 √ 7 • 2, 4, 6 ÷ 2, 2, 7 π

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3there are some others too.... but these are useful examples

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So if it was x=6 would the outer radius be 2+y^2 and the inner radius be 2?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3if it was x=6, dw:1441596092489:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Do you mean, if it was a region of y^2 bound by y=0 and x=4, but rotated about x=6?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Yes, then your radius is y²+2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3and if you rotated in a same case about y=4+c then your radius is y²+c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought I had to subtract the inner area?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3yeah, my bad, I am overheating let me think

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441596258832:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441596426856:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For this problem I can only use washer

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Oh, you can do it with respect to x, and do f(x)g(x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3But, shell is also good.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3it is a matter of preference

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Would f(x) be y^2+2 and g(x) be 2?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{2} (2+y^2)^2(2)^2\] ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3lets rvw the washer with x's

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441596741353:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3of that integral should say π INTEGRAL f(x)²g(x)² dx

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just don't understand what g(x) would be in this situation

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3and with y, you get the same thingdw:1441596949137:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3the area of the cylinder with h=2, r=2 is 8π

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Or you can say that g is 2.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3if instead of 4, you had some z(x) boundary for the region, then the radius for g would be 6z(x) (of course from y=0 to y=2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay I think I understand this better now thank you

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Anytime... thank you for refreshing me on these rotations:)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I mean, I really should tell you that Shell method rocks in so many cases, so try to use that as well. in any case, good luck!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Actually, did I plug this in incorrectly? http://www.wolframalpha.com/input/?i=integrate+from+0+to+2+pi%28%282%2By%5E2%29%5E24%29

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The answer is 192π/5

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3for the problem where you want to know about the redion of y62 bound by y=0 and x=4, rotated about x=6....?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3dw:1441597714083:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I actually do not get why the answer isn't what you got in wolfram.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3you can take the whole volume of radius y^2+2 with limits of y=0 to y=2, and subtract 8π cylinder in the middle, and you get precisely the same.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I have to go, it is almost 12am in my location. maybe I was answering a wrong question idk, but for what I asked, it should be 256π/15

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3Maybe my brain just shot down xD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But I really appreciated your time so thank you

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.3I will look at it when I have time. Whatever I can do with my little knowledge:) gtg c(u)
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