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5. Very few functions y = f(x) lead to integrands of the form v/1 + (dy/dx) which have elementary antiderivatives. In problem 5, 1 + (dy/dx)? is a perfect square and the resulting arc length integrals can be evaluated using antiderivatives. Do so. 1 + 16x4 . for 4 5 x s 25. Directions for problem 6: (a) represent the length as a definite integral, and (b) evaluate the integral using your calculator's integral command. 6. As a tire with a 1-foot radius rolls forward 3 miles, how far does a pebble stuck in the tire tread travel? (x(t) = 1(t - sin(t))and y(t) = 1(1 - cos(t)). 7. The conical container in Fig. 18 is filled with loose grain which weighs 40 pounds/ft'. Show work. (a) How much work is done lifting all of the grain over the top of the cone? (b) lifting the top 2 feet of grain over the top of the cone? Fig. 18