# 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 This solution is **FREE** courtesy of BrainMass!

(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 B,

So @ A and B, f(x)=g(x)

A=2.437047

B=5.769904

(a)

Washers:

Volume of the shape which is formed if R is rotated around the x-axis

The volume is 180.663.

(b)

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

Using the cylindrical shells method, the volume is , here r=x-(-2) since it is rotated around the line x=-2. h=f(x)-g(x);

The volume is 263.747.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:53 pm ad1c9bdddf>https://brainmass.com/math/integrals/volume-solid-revolution-77438