Written Homework $7$: Submitting this assignment is optional, but it will be worth $10$ points extra credit in the "Written HW$"$ category of your gradebook.

Note: You will learn how to do problems $4$ and $5$ in class on Friday, Dec $6.$

A cattle trough has a trapezoidal cross section with a height of $1$ meter $($ m $),$ length $10$ m $,$ and horizontal sides of length $\frac{1}{2}m$ and $1$ m $.$ See image below. Set up $($but do NOT evaluate$)$ the integral needed to determine the required to pump the water out of the full trough over the top edge

Using the full trapezoidal trough in problem $1.,$ set up $($but do NOT evaluate$)$ the integral needed to determine the work required to pump the water out of the trough until the depth is $0\mathrm{.}25$ m $.$