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Mertsj
 3 years ago
Find the volume of the solid obtained by rotating the region bounded by x=0 and x = 9y^2 about the line x=1
Mertsj
 3 years ago
Find the volume of the solid obtained by rotating the region bounded by x=0 and x = 9y^2 about the line x=1

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TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1330221858790:dwI think judging by the picture the way to go is the socalled 'washer method' the graph of x=9y^2 intersects the line x=0 at y=3 and y=3, so those will be our bounds of integration now for the radii...

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1330222034408:dwthe outer radius will be from x=1 to f(y), so the distance is ro=f(y)(1) the inner radius is from x=1 to the xaxis, so that is 1 here is an overhead view of each washer that we will usedw:1330222180739:dwso the integral will be\[\pi\int_{a}^{b}r_o^2r_i^2dy=\pi\int_{3}^{3}(f(y)+1)^21^2dy\]\[=\pi\int_{3}^{3}(10y)^21dy\]

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.2whoops, typo on the last integral (forgot to that y is squared): \[V=\pi\int_{a}^{b}r_o^2r_i^2dy=\pi\int_{3}^{3}(f(y)+1)^21^2dy\]\[V=\pi\int_{3}^{3}(10y^2)^21dy\]and since this integrand is even we can write\[V=2\pi\int_{0}^{3}(10y^2)^21dy\]

Mertsj
 3 years ago
Best ResponseYou've already chosen the best response.5Thanks Turing. You are awesome!!
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