DIRECTIONS: Show as much work as possible within each question as I grade on both the process and the final answer. TI-89's are wonderful calculators, but they don't show me if you know anything about calculus! Show all work.
1. (6 pts each) Determine the following antiderivatives (don't worry about simplifying, just show the rules)
2. (6 pts each) Calculate the value of each definite integral (Show work!):
3. (6 pts each) a. Approximate the area under the curve and above the x-axis by splitting the region from to into 4 equal subintervals (rectangles) and using the midpoints of the subintervals as the heights.
b. Use the Simpson's Rule with to estimate area under the curve
c. Find the exact value of , and compare with the answer obtained from part (a), and (b). Which method is more accurate, part A or part B?
4. (8 pts) Determine the area between the curves and
5. (6 pts) Use geometry to determine the value of the following definite integral:
6. (8 pts) A stock analyst plots the price per share of a certain stock as a function of time and finds that it can be modeled by the function where t is the time (in years) since the stock was purchased. Find the average price of the stock over the first 2 years of its purchase.
7. (8 pts) Use the consumer's surplus formula to determine the consumer's surplus for the demand equation if we assume supply and demand are in equilibrium when
8. (8 pts) Sketch the region and then calculate the volume of the solid of revolution formed by rotating the region bounded by , , and around the x-axis.
9. The function represents the rate of flow of money in dollars per year. Assume a 8-year period for t and a rate r of 10% compounded continuously and determine the following:
a. (6 pts) The present value
b. (2 pts) The accumulated amount
The solutions are provided in a jpg file. Step-by-step computations are shown.