Calculus

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Directions: Solve all problems. Show your work on this paper, scan your work into a single PDF file (name your file: lastnameExam4.PDF) and email your work to [email protected] by Wed., 4/28, 12noon.

1. Find the indefinite integral .

2. Find the area of the region bounded by the graphs of the equations . Round your answer to the nearest whole number.

3. The volume V in liters of air in the lungs during a five-second respiratory cycle is approximated by the model where t is the time in seconds. Approximate the average volume of air in the lungs

during one cycle. Round your answer to four decimal places.

4. Find given .

a.

b.

c.

d. e.

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5. Find the indefinite integral .

6. Find the indefinite integral .

7. The graph of f consists of line segments, as shown in the figure. Evaluate the definite integral using

geometric formulas.

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8. Determine the area of the given region.

9. Find the indefinite integral.

10. Evaluate the definite integral.

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11. Find if .

12. Suppose the demand equation for a product is . Find the average price p on the interval .

Round your answer to the nearest dollar.

13. The rate of change of an income flow is given by the function 𝑓𝑓(𝑡𝑡) = 20 𝑒𝑒𝑡𝑡

. If the rate is given by 𝑟𝑟 = 3%, find 𝑃𝑃𝑣𝑣(4).