Question

Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes.

x = y - y3, x = 1, y = 1

(b) Revolved about the y-axis ?


Hi Shawn,

97/105 * pi ?

:)

We need to cut away the volume of the region you get by revolving the area inbetween the y-axis and the line x = y - y^3 from the "total volume" you get by revolving the entire square bounded by the x-axis, the y-axis the line x = 1 and the line y = 1. The latter is pi. The former is:

pi * Integral from zero to 1 of dy (y - y^3)^2 =

pi*(1/3 - 2/5 + 1/7) = 8/105*pi

The volume is thus pi - 8/105*pi = 97/105 * pi

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Anonymous,this is not a social site.This is for help not for you to post gggggggggggggggggggggggggg repeatedly.