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Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curve...Asked by Mark
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 1 + (y − 6)^2, x = 17
x = 1 + (y − 6)^2, x = 17
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Answered by
oobleck
The curves intersect at (17,2) and (17,10)
v = ∫[2,10] 2πrh dy
where r=y and h=17-x = 17-(1+(y-6)^2)
v = ∫[2,10] 2πy(17-(1+(y-6)^2)) dy = -2π∫[2,10] (y^3-12y^2+20y) dy
v = ∫[2,10] 2πrh dy
where r=y and h=17-x = 17-(1+(y-6)^2)
v = ∫[2,10] 2πy(17-(1+(y-6)^2)) dy = -2π∫[2,10] (y^3-12y^2+20y) dy