(Solved): verify the integration formula  The rectangular tank shown here. with its lop of gound level, ...

The rectangular tank shown here. with its lop of gound level, is used to catch runofl water. Aasume that the wataf welghis \( 07.4 \mathrm{hr} \) h? a. How much work does it take to emply the tank by pumping tho waker bock fo ground level once the tark is fur? Will it take to enipy the tank to the nearest minulo?? c. Show that the pump in parl (B) will lower the water lovel 10 ff (halliay) during the fist 22 mirules of purnping d. What are the arswers to parts (a) and (b) in a location where water weighs \( 62.16 \mathrm{~b} / \mathrm{\pi}^{3} ? 62.62 \mathrm{ta}_{2} / \mathrm{H}^{3} \) ? \[ w=\int d y \] How much work does it thie to emply the tank? Verify the integration formula below. \[ \int x \operatorname{coth}^{-1} x d x=\frac{x^{2}-1}{2} \operatorname{coth}^{-1} x+\frac{x}{2}+C \]