# Rotation of integrals

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Find the volume of a solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse *See attached for equation*

and the x-axis and thus find the volume of a prolate spheroid. Here a and b are positive constants, with a<b

Volume of the solid of revolution:

Please see attachment for details

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#### Solution Preview

(x^2/a^2) + (y^2/b^2) = 1

Ellipse with major axis x = -a to +a and minor axis y = -b to +b

So, y^2 = [ 1 - (x^2/a^2)]*b^2 ---(1)

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#### Solution Summary

The expert finds the volume of a solid generated by revolution. The volume of the solid of revolution is given.

$2.49