Reference no: EM13899499

1. Determine the following antiderivatives (don't worry about simplifying, just show the rules)

a. ∫(x²⁰⁰+√x-e^2Πx)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 ₀^qo∫[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= ₀^t∫f(x)e^-rxdx)

b. The accumulated amount (A= e^rt ₀^t∫f(x)e^-rxdx)