# Volume of solid of revolution

Let R be the region bounded by the curves f(x) = ln(x+3) +2 and

g(x) = x^2 - 8x + 18.

a) Using the washer method, find the volume of the shape which is formed if R is rotated around the x- axis.

b) Using the cylindrical shells method, find the volume of the shape which is formed is R is rotated around the line x = -2.

Show all work including the integrals used and the limits of integrations.

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#### Solution Preview

(a) The volume is 180.663.

(b) The volume is 263.747.

Details are in the attached word file.

Assume f(x) and g(x) intersect at A and ...

#### Solution Summary

This solution is comprised of a detailed explanation of calculation of the volume of revolving solid by washer and shell method. Supplemented with diagrams, this step-by-step explanation of this complicated topic provides students with a clear perspective of application of integration.