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anonymous
 4 years ago
what is the volume of the region bounded by y=e^x^2, y=0, x=0, and x=2 when it is rotated around the y axis?
anonymous
 4 years ago
what is the volume of the region bounded by y=e^x^2, y=0, x=0, and x=2 when it is rotated around the y axis?

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0I don't really see how to integrate this is this how the problem was given originally? or did you get this function from somewhere?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ya thats the equations we were given :/

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2dw:1327620023966:dw the volume is sum of the crosssectional areas from 0 to 1. each area is a circle with radius of x. From y=0 to e^4, the radius is constant at 2 y = e^x^2 lny = x^2 ln(y) = x^2 Area = pi*r^2 = pi*x^2 = pi*ln(y) \[\large V = \pi \int\limits_{0}^{e^{4}} 4 dy + \pi \int\limits_{e^{4}}^{1}\ln (y) dy\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0where did you get the first integral from?

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2\[= 4\pi e^{4} \pi \ln(y)(y1) {e^{4} \to 1}\] ... from the part where radius is a constant 2 pi*2^2 = 4pi

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ahhh ok i see makes sense. thank you very much i was having problems with this question lol

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0me too, nice one dumbcow :D
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