In problems 7-12, represent each volume as an integral and evaluate the integral. squares 7. Fig. 34. For 0x3, each face is a rectangle with base 2 inches and height 5-x inches. Fig. 34 y-5-x Fig. 36 1: 8. Fig. 35. For 0x3, each face is a rectangle with base x inches and height x inches. 9. Fig. 36. For 1 PROBLEMS For are length 1. A squirrel was spotted at the backyard locations in Table 1 at the given times. The squirrel traveled at least how far during the first 15 minutes? time location relative to oak tree (min) north east (feet) 0 10 7 5 25 27 10 1 45 15 13 33 20 24 40 25 10 23 30 0 14 2. The squirrel in Problem 1 traveled at least how far during the first 30 minutes? Locations of Squirrel 3. Use the partition {0,1,2} to estimate the length of y = 2* between the points (0, 1) and (2,4). 4. Use the partition {1,2,3,4} to estimate the length of y = 1/x between the points (1, 1) and (4, 1/4). The graphs of the functions in problems 5-8 are straight lines. Calculate each length (a) using the distance formula between 2 points and (b) by setting up and evaluating the are length integrals. 5. y 1+2x for 0x2. 7. x=2+1,y=1-21 for 0sts3. 6. y 5-x for 1sxs4. 8. x=-1-4t,y=2+t for 1sts4. 9 Calculate the length of y = 3 x3/2 for 0x4. 4. A cylindrical aquarium with radius 2 feet and height 5 feet (Fig. 16) is filled with salt water (65 pounds/ft). (a) How much work is done pumping all of the water over the top edge of the tank? (b) How much work is done pumping the water to a point 3 feet above the top edge of the tank? 5 (c) How long does a 1 horsepower pump take to empty the tank over the top edge of the tank? A 1/2 horsepower pump? Which pump does more work? Fig. 16 4. (a) Find the total mass and the center of mass for a system consisting of the 4 masses in Table 6. (b) Where should you locate a new object with mass 12 so the new system has its center of mass at (3,5)? 61235 m x y 5213 5 4 7 1 0 3 8 Table 6