Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=4x^2−x^3 and y=0.

Question

Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=4x^2−x^3 and y=0.

(a)   A typical shell has radius x, circumference 2πx, and height f(x)=   

(b)   So, by the shell method, the volume is V=∫a0  dx  and a= 

(c)   Evaluate the integral: V=

Answer 1

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