Mass density of water in a horse trough = 1000 kg/m³, weight density of water = 9800 N/m³.

1. A mathematician designs a funnel to fill his horse trough. The funnel is infinitely long. In fact, it can be described by rotating the curve about the x axis for x between 1 and infinity. Find the volume of the funnel.




2. A mathematician designs a horse trough of infinite length whose cross sections are rectangles of width one

centimeter and height centimeters. If the trough is filled with water, is the mass of the water infinite or finite? Hint, the mass of water in the trough in grams is given by . If the integral converges, estimate its value to within 3 decimal places.






3. The ends of a horse trough 319 meters long are equilateral triangles having sides of length 2 meters. If the horse trough is full of water, find the hydrostatic force on one end of the trough.






4. The ends of a horse trough 10 meters long are semi-circles of radius 2 meters. If the horse trough is full of water, find the work required to pump all of it into another horse trough 10 meters above the top of the trough.







5. You were kicked out of your dorm because you had a horse trough full of ice in your room for chilling beverages. Now you are homeless and must sleep in your horse trough. However, a manufacturer of horse troughs offers you a job if you can just evaluate the improper integral .

6. You are driving your pickup, with a horse trough in the back, when suddenly you see a four car pile up
ahead. (No horse troughs were injured.) Compute the improper integral . If it diverges just say so, if it converges, find its value.


7. The region bounded by the curves y = x and y = x2 is rotated about the line y = 3. Compute the volume of the resulting solid (note the following would make a poor horse trough, cuz there's a hole in it.)