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Cameronmx9
 3 years ago
Find the volume of the solid generated by revolving the region bounded by the curves y =sqrt(x)
and y = x  2 and the line x = 0 around the yaxis
Cameronmx9
 3 years ago
Find the volume of the solid generated by revolving the region bounded by the curves y =sqrt(x) and y = x  2 and the line x = 0 around the yaxis

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Hunus
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1327635566351:dw The equation needs to be with respect to y The radius of the outer part of the solid of revolution is (y+2) and the radius of the inner is y^2 So the area of each cross section is \[\int\limits_{1}^{2}(\pi(y+2)^2  \pi(y^2)^2)dy=\pi \int\limits_{1}^{2}((y^2+4y+4)  (y^4))dy\] \[\pi \int\limits_{1}^{2}((y^2+4y+4)  y^4)dy=\pi \left[ \frac{y^3}{3} + 2y^2 + 4y\right]_{1}^{2}\] \[\pi \left[ \frac{y^3}{3} + 2y^2 + 4y\right]_{1}^{2} = \pi \left[( \frac{8}{3} + 8 + 8)(\frac{1}{3}+24)\right]\] \[\pi \left[( \frac{8}{3} + 8 + 8)(\frac{1}{3}+24)\right]=21\pi\]
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