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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

exraven
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.01 sec,I need to process that.

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

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

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

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

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

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

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

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

exraven
 2 years 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
 2 years 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
 2 years 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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