Question

Use cylindrical shells to find the volume of the solid that results when the red region is revolved about the y

y-axis. f(x)=x^2 ,a=1 ,b=4

Answer 1

$V=\int_a^b 2\pi x f(x) dx\\ V=2\pi\int_1^4x^3dx\\ V=2\pi\left[\frac{x^4}{4}\right]_1^4\\ V=2\pi(64-\frac{1}{4})\\ V=\frac{255}{2}\pi$