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 one year ago
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 5.
y=x^2 , x=y^2
 one year ago
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 5. y=x^2 , x=y^2

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Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Anyone want to help me set up the intergal? I can do the rest.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2sketch the region first

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0dw:1358400866711:dwI did:

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Something like that roughly.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2can you determine the radius and the height?

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0No I can't actually lol.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2the radius and the height must be a function of y

exraven
 one year ago
Best ResponseYou've already chosen the best response.2the height is the rightmost curve minus the leftmost curve right?

exraven
 one year ago
Best ResponseYou've already chosen the best response.2the height must also be a function of y

exraven
 one year ago
Best ResponseYou've already chosen the best response.2actually its not like that, wait ill draw again

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Allright. Thanks for thing the timet o help me :) . Really hard vizualzing all this stuff.

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Right  left the I suppose right?

exraven
 one year ago
Best ResponseYou've already chosen the best response.2yes, but it must be a function of y

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Same function regardless right?

exraven
 one year ago
Best ResponseYou've already chosen the best response.2because we integrate it with respect to y later

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I see it now haha.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2and here is the way to determine the radiusdw:1358402147166:dw the radius is y + 5

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0the limits would be from 0 to 1 I believe or am I wrong?

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0The radius would simply be the parbola  the line.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2\[\Delta V = 2 \pi R h \Delta y\]\[\Delta V = 2 \pi (y + 5)(\sqrt{y}  y^2) \Delta y\]\[V = \int\limits_{0}^{1} 2 \pi (y + 5)(\sqrt{y}  y^2) dy\]

Dido525
 one year ago
Best ResponseYou've already chosen the best response.01 sec,I need to process that.

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Woudn't it b sqrt(y)+5?

exraven
 one year ago
Best ResponseYou've already chosen the best response.2this is for the radiusdw:1358403009035:dwthis is for the heightdw:1358403125789:dw

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0The answer I got was 2 which is wrong.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2feel free to ask if its hard to follow

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Why isn't the height sqrt(x)+5?

exraven
 one year ago
Best ResponseYou've already chosen the best response.2it must be a function of y, because we integrate it with respect to y, sqrt(x) + 5 = y + 5

exraven
 one year ago
Best ResponseYou've already chosen the best response.2and it is not the height, it is the radius

exraven
 one year ago
Best ResponseYou've already chosen the best response.2the radius is sqrt(y)  y^2

Dido525
 one year ago
Best ResponseYou've already chosen the best response.0Ahh, that distance is y and add 5.

exraven
 one year ago
Best ResponseYou've already chosen the best response.2yup, its sqrt(x), because the curve is x = y^2 sqrt(x) = sqrt(y^2) = y

exraven
 one year ago
Best ResponseYou've already chosen the best response.2yes, because the cylinder looks like thisdw:1358404151779:dwwe integrate it with respect to y, because we fill the cylinder downward

exraven
 one year ago
Best ResponseYou've already chosen the best response.2here is more details, I am sorry if I cannot explain further, because I teach myself all this stuff http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithCylinder.aspx
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