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 horizontal line y = 5.
A) 23.93 $\pi$
B) 32.93 $\pi$
C) 27.93 $\pi$
D) 29.93 $\pi$

Question

Quizplus · Accepted Answer

The volume of the solid formed by revolving the region between $y = x^2 + 1$ and the x-axis from $x = 0$ to $x = 2$ around the line $y = 5$ can be found using the disk method. The radius of a typical disk is the distance from $y = 5$ to $y = x^2 + 1$, which is $5 - (x^2 + 1) = 4 - x^2$. The volume of the solid is given by the integral $\int_{0}^{2} \pi (4 - x^2)^2 dx$. When you compute this integral, you get $32.93 \pi$.

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 $f ( x ) = x ^ { 2 } + 1$