Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x-axis. $y=x^{2}, y=0, x=1, x=4 ; \text { about } x=1$
A) $\frac{255 \pi}{2}$
B) $3413 \pi$
C) $1020 \pi$
D) $\frac{2 \pi}{255}$
E) $255 \pi$

Question

Quizplus · Accepted Answer

The method of cylindrical shells involves integrating the product of the circumference of the shell, the height of the shell, and the thickness of the shell. The integral setup for this problem is $\int_{1}^{4} 2\pi (x-1)(x^2) \, dx$, which evaluates to $\frac{255 \pi}{2}$.

Use the Method of Cylindrical Shells to Find the Volume y=x2,y=0,x=1,x=4; about x=1y=x^{2}, y=0, x=1, x=4 ; \text { about } x=1y=x2,y=0,x=1,x=4; about x=1

Use the Method of Cylindrical Shells to Find the Volume $y=x^{2}, y=0, x=1, x=4 ; \text { about } x=1$