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When we revolve the area bounded by y = x 4 , y = 4, and...

When we revolve the area bounded by y = x 4 , y = 4, and x = 0 about the y-axis, we get a volume resembling a tank. We will calculate the work required to pump fluid out of this tank given by W = R (area)(density)(distance).

(a) Sketch this tank.

(b) Start by calculating the area of a horizontal disk.

(c) Now, find the distance we have to move this disk to get it out of the tank.

(d) Finally, assume the density of the fluid is 15. Write down an integral representing the work required to pump all the fluid out of this tank if the tank is full (you don’t need to evaluate the integral). 1 2. Consider the tank obtained by revolving the area bounded by y = 3x, y = 6, and x = 0 about the y − axis

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