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.
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.