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 $\pi\left(4-x_{i}\right)^{2}$. Set up, but do not evaluate, an integral representing the volume of this solid.
$\int_{0}^{4} \pi(4-x)^{2} d x$
$\int_{0}^{4} \pi\left(4-x_{i}\right)^{2} \Delta x d x$
$\int_{0}^{4} \pi\left(4-x_{i}\right)^{2} d x$
$\int_{0}^{4} \pi(4-x)^{2} \Delta x d x$

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 \(\pi\left(4-x_{i}\right)^{2}\).

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 \(\pi\left(4-x_{i}\right)^{2}\) and the range is from 0 to 4 on the x-axis.

Step 4 ：Therefore, the volume can be represented by the integral \(\int_{0}^{4} \pi\left(4-x_{i}\right)^{2} dx\).

Step 5 ：Final Answer: The integral representing the volume of the solid is \(\boxed{\int_{0}^{4} \pi\left(4-x\right)^{2} dx}\).