Let Q Q be the region in the first quadrant enclosed by y=x4−16 y = \sqrt{$$x^4 - 16$$} , y=0 y = 0 , and y=4 y = 4 . This region is revolved around the y y -axis to form a tank, which is then completely filled with water. How much work is required to pump all the water up to the top of the tank? Assume that the variables x x and y y are measured in meters. Use ρwater=1000 kgm3\rho_{\text{water}}=1000~\frac{\text{kg}}{\text{m}^3} and g=9.8 ms2g=9.8~\frac{\text{m}}{\text{s}^2}.

313600π(ln⁡(1+2)−2−23) J313600\pi\left(\ln\left(1+\sqrt2\right)-\frac{\sqrt2-2}{3}\right)~\text{J}

313600π(ln⁡(2+2)−2−13) J313600\pi\left(\ln\left(2+\sqrt2\right)-\frac{\sqrt2-1}{3}\right)~\text{J}

156800π(ln⁡(1+2)−2−23) J156800\pi\left(\ln\left(1+\sqrt2\right)-\frac{\sqrt2-2}{3}\right)~\text{J}

156800π(ln⁡(2+2)−2−13) J156800\pi\left(\ln\left(2+\sqrt2\right)-\frac{\sqrt2-1}{3}\right)~\text{J}

Let Q Q be the region in the first quadrant enclosed by y=x4−16 ...

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