Answer:
![V = \pi [4√(2) -(8√(2))/(3) +1.131] =9.478](https://img.qammunity.org/2021/formulas/mathematics/college/vnf1a5ld2ecejm51e5huuijcp2u32ach5o.png)
Explanation:
For this case we have the following function
bounded by
. The area of interest is on the figure attached.
For this case we can calculate the volume using the method of rings. First we can calculate the area like this:

And the volume can be founded with the following formula:

For this case we need to find the intersection point with the x axis, and we can do this:

, but for our case would be just the positive value, So then we can find the volume like this:

And if we do the integral we got this:
![V = \pi [4x -(4)/(3)x^3 +(x^5)/(5) \Big|_(0)^(√(2))]](https://img.qammunity.org/2021/formulas/mathematics/college/rgtv36ipjyxvhg54ewl3e9e1q11kwm4vm0.png)
And when we apply the fundamental theorem of calculus we got:
![V = \pi [(4√(2) -(4)/(3) (√(2))^3 +((√(2))^5)/(5)) -(0)]](https://img.qammunity.org/2021/formulas/mathematics/college/v7wk0ybe5egumeow787mji0p928oyygd7v.png)
![V = \pi [4√(2) -(8√(2))/(3) +1.131] =9.478](https://img.qammunity.org/2021/formulas/mathematics/college/vnf1a5ld2ecejm51e5huuijcp2u32ach5o.png)