Consider the region between the graph of $f ( x ) = x ^ { 2 } + 1$ and the x-axis on the interval [0, 2].
-Use disk/washer method to construct definite integrals to find the volume of the solid that is obtained by revolving this region around the vertical line x = 2.
A) 4.66 $\pi$
B) 6.66 $\pi$
C) 8.66 $\pi$
D) 9.66 $\pi$

Question

Quizplus · Accepted Answer

The volume of the solid obtained by revolving the region between the graph of $f(x) = x^2 + 1$ and the x-axis on the interval [0, 2] around the vertical line $x = 2$ can be found using the disk method. The radius of a disk at a point $x$ is $2 - x$, and the height of the disk is $f(x) = x^2 + 1$. The volume is given by the integral $\pi \int_{0}^{2} (2 - x)^2 (x^2 + 1) dx$. Simplifying and calculating this integral gives a volume of $6.66 \pi$.

Consider the Region Between the Graph Of f(x)=x2+1f ( x ) = x ^ { 2 } + 1f(x)=x2+1

Consider the Region Between the Graph Of $f ( x ) = x ^ { 2 } + 1$