Exam 13: Definite Integrals - Techniques

The demand function for a product is and the supply function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus there. Round to the nearest cent. ​

Suppose spending for a wireless communications services (in billions of dollars per year) can be modeled by the function where represents 1995. Use equal subdivisions with right-hand endpoints to approximate the area under the graph of S(t) between and . Round your answer to one decimal place. ​

Evaluate the integral by integration. Round your answer to two decimal places. ​

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places. ​

Equations are given whose graphs enclose a region. Find the area of the region. ​ , , and ​

Evaluate the integral . ​

A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Find the present value of the Video Palace over the next 8 years (until the couple reach age 66). Round your answer to the nearest dollar. ​

Evaluate the integral . ​

A franchise models the profit from its store as a continuous income stream with a monthly rate of flow at time t given by (dollars per month). When a new store opens, its manager is judged against the model, with special emphasis on the second half of the first year. Find the total profit for the second 6-month period to . Round your answer to the nearest dollar. ​

Evaluate the improper integral if it converges, or state that it diverges. ​

Find the area between the curve and the x-axis from to . ​

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places. ​

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent. ​

Evaluate the integral .

Find the average value of the function ​

Use an integral formula to evaluate . ​

Evaluate the integral . ​

Suppose that the profit from a machine's production can be considered as a continuous income stream with annual rate of flow at time t given by (dollars per year). If money is worth 14%, compounded continuously, find the present value of this stream over the next 5 years. Round your answer to the nearest dollar. ​

For the interval [-5,2] and for n = 3 find h.

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​