Question 3
1 pts
Suppose that you have a solid whose bounds on the $x$-axis are 0 and 4 , and whose cross-sectional area of the $x_i$ th slice is given by $\pi {(4-x_i)}^2$. Set up, but do not evaluate, an integral representing the volume of this solid.
${\int }_0^4\pi (4-x{)}^{2}dx$
${\int }_0^4\pi {(4-x_i)}^2\mathrm{\Delta }xdx$
${\int }_0^4\pi {(4-x_i)}^{2}dx$
${\int }_0^4\pi (4-x{)}^2\mathrm{\Delta }xdx$

Step 1 ：Suppose that you have a solid whose bounds on the x-axis are 0 and 4, and whose cross-sectional area of the $x_i$ th slice is given by $\pi {(4-x_i)}^2$.

Step 2 ：Set up, but do not evaluate, an integral representing the volume of this solid.

Step 3 ：The volume of a solid can be calculated by integrating the cross-sectional area over the range of the solid. In this case, the cross-sectional area is given by $\pi {(4-x_i)}^2$ and the range is from 0 to 4 on the x-axis.

Step 4 ：Therefore, the volume can be represented by the integral ${\int }_0^4\pi {(4-x_i)}^{2}dx$.

Step 5 ：Final Answer: The integral representing the volume of the solid is $\boxed{{\displaystyle {\int }_0^4\pi {(4-x)}^{2}dx}}$.