1. Determine the following antiderivatives (don't worry about simplifying, just show the rules)
a. ∫(x200+√x-e2Πx)dx
b. ∫x(4x2- 3)47dx
c. ∫(3/x+5/x4-8)dx
2. Calculate the value of each definite integral (Show work!):
a. 01∫(x2/2x3+9)dx
b. 24∫x2(6x3+3)dx
c. 2∞∫3/x4dx
3. a. Approximate the area under the curve f(x)=1/√x and above the x-axis by splitting the region from x= 1 to x= 9 into 4 equal subintervals (rectangles) and using the midpoints of the subintervals as the heights.
b. Use the Simpson's Rule with n=4 to estimate area under the curve f(x)=1/√x
c. Find the exact value of 19∫1/√xdx , and compare with the answer obtained from part (a), and (b). Which method is more accurate, part A or part B?
4. Determine the area between the curves f(x)= x2-2 and g(x)=x
5. Use geometry to determine the value of the following definite integral: -33∫√9-x2dx
6. 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 S(t)=25-5√10t 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. Use the consumer's surplus formula 0qo∫[D(q)-p0]dq to determine the consumer's surplus for the demand equation D(q)=1400-50q if we assume supply and demand are in equilibrium when q=15.
8. Sketch the region and then calculate the volume of the solid of revolution formed by rotating the region bounded by f(x)=x2+3 , y=0 ,x=1 and x=5 around the x-axis.
9. The function f(x)=240 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. The present value (P= 0t∫f(x)e-rxdx)
b. The accumulated amount (A= ert 0t∫f(x)e-rxdx)