Question

Find the volume of the figure created by rotating the region enclosed by the graphs of y = x^2 and y = x^3

a) around the x-axis

b) around the y-axis

Answer 1

(a)

Region is bounded by

,

For the region,

Volume of the solid formed by revolving the region about x-axis by washer method is given by

From ,

From ,

That is

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(b)

Region is bounded by

,

For the region,

Volume of the solid formed by revolving the region about x-axis bu washer is given by

From ,

From ,

That is

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