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# Volume of solid of revolution

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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.

https://brainmass.com/math/integrals/volume-solid-revolution-77438

## 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.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!