Show that Jax dx =-(b2-a2) using Definition of Definite Integral (limit of a Riemann Sum) Fundamental Theorem of Calculus a. b. 2) The water level (in feet) in Boston Harbor during a certain 24-hour period is approximated by the formula H = 4.8 sin]" (t-10)| + 7.6, 0 t 24 where t 0 corresponds to 12 a. What is the average water level in Boston Harbor over the 24-hour period on that b. At what times of the day did the water level in Boston Harbor equal the average A.M day? water level? (Use Mean Value Theorem for Integrals) 3) Newton's Law of Cooling. A bottle of white wine at room temperature (70°F) is placed in a refrigerator at 3 P.M. Its temperature after t hours is changing at the rate of -18e-65t oF/hr a. By how many degrees will the temperature of the wine have dropped by 6 P.M.? b. What will be the temperature of the wine be at 6 P.M.? c. Sketch graphs of the functions n(t)-18e6St °F/hr, and its antiderivative N(t) d. Where on the graphs of n(t) and N(t) can the solution to part (a) be found? Point them out. And why does it make sense that N(t) has a horizontal asymptote where it does? 4) cos 2x dx on [0, Ï ] Use the Trapezoidal Rule to approximate the integral with n 6. Then, to check your solutions, use the Fundamental Theorem of Calculus. Do the answers make sense? Explain 5) Evaluate the integral sinx cosx dx by two methods: first by letting u-sinx; and then by letting u=cosx. Explain why the apparently different answers are really equivalent.