Y=x^3 Y=0 X=1 About X=2

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

y = x3, y = 0, x = 1; about x = 2

Answer

y=x^3 y=0 x=1 about x=2

 

When we rotate a thin vertical strip as shown in the figure, about the line x = 2.

We get a cylindrical shell with a radius 2 – x

The height of the cylindrical shell is x^3

To find the complete volume, we will integrate from 0 to 1,

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