9. Find the area enclosed by the curves f (x) = x2 - 4x and g(x) = x + 6. Start by drawing a graph and shading the area that you are looking for. 12 10 $ 10 12 12 10. Suppose that the supply function for some commodity is p = (q + 1) and the demand function for the commodity is p =- 1000 9+1 a. Find the producers' surplus.11. A stock analyst plots the price per share of a certain common stock as a function of time and finds that it can be approximated by the function f(t) = 25 - 5e-0:015, where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first five years. Round your final answer to two decimal places if needed. 12. If money is flowing continuously at a constant rate of $1000 per year over 4 years at 5% compounded continuously, find the integral for the present value of the amount. (You don't need to evaluate it.) 13. The rate of a continuous flow of money starts at $1000 and increases exponentially at 5% per year for 4 years. If the interest rate is 3.5%, find: a. The present value of the amount. b. The accumulated amount of the money flow.14. Determine whether each improper integral converges or diverges, and find the value if it converges. a. dx b. Be Bx dx 15. Find each of the following integrals. a. [4x(x2 + 7)5 dx b. | 4x(x + 7)5 dx c. [ 4x(x + 7) dx