Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the graph of f(x) = 4x3+12x2 about the y-axis on the interval [-3, 0]. Please show all steps and retain pi.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 25E
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Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the graph of

f(x) = 4x3+12x2 about the y-axis on the interval [-3, 0]. Please show all steps and retain pi. 

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