(Solved): Note that for this exercise (0,0) is at the bottom of the tank. A tank with cross-sectional are ...

Note that for this exercise $$(0,0)$$ is at the bottom of the tank. A tank with cross-sectional area the shape of an isosceles trapezoid is shown below. Suppose the height of the tank is $$H=5\mathrm{m}$$, the width at the top is $$W=3\mathrm{m}$$, the width at the bottom is $$B=1\mathrm{m}$$, the overall length is $$L=9\mathrm{m}$$, and the pipe coming out of the top of the tank is $$P=0.9\mathrm{m}$$. Moreover, suppose the tank is initially only partially filled with brine to a depth of $$D=1\mathrm{m}$$. a. Set up an integral with respect to $$y$$ representing the amount of work necessary to completely empty the tank. You will need to use the facts that the denisty of brine is $$1230\mathrm{kg}/{\mathrm{m}}^3$$ and the acceleration due to gravity is $$9.8\mathrm{m}/{\mathrm{s}}^2$$. Answers should be in exact form (i.e., do not use a calculator to get a decimal approximation). $$\begin{array}{l}y=\\ y=\end{array}dy$$ b. Evaluate your integral from part a. Round your answers to the nearest whole number. $$W=$$