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Section 4.2

Section 4.2. 1. Find the indefinite integral. 2. Find the indefinite integral. 3. Find the indefinite integral. 4. Find the indefinite integral. Use the rule ∫ 1/x dx = ∫ x - 1 dx = ln |x| + C. 5. Find the indefinite integral. Use the rule ∫ 1/x dx = ∫ x - 1 dx = ln |x| + C.

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Section 4.2

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  1. Section 4.2 1. Find the indefinite integral.

  2. 2. Find the indefinite integral.

  3. 3. Find the indefinite integral.

  4. 4. Find the indefinite integral. Use the rule ∫ 1/x dx = ∫ x - 1 dx = ln |x| + C

  5. 5. Find the indefinite integral. Use the rule ∫ 1/x dx = ∫ x - 1 dx = ln |x| + C

  6. 6. Find the indefinite integral.

  7. 7. Find the indefinite integral.

  8. 8. Find the indefinite integral.

  9. 9. Find the indefinite integral.

  10. 10. Find the indefinite integral.

  11. 11. Find the indefinite integral.

  12. BIOMEDICAL: Epidemics: A flu epidemic hits Beard Hall, beginning with five cases on day t = 0. the rate of growth of the epidemic is given by • r(t) = 18e 0.05t where t is the number of days since the epidemic began. • a. Find a formula for the total number of cases of flu in the first t days. • b. Use your formula to find the total number of cases in the first 20 days. a. To find a formula for the number of cases of flu, integrate r(t). Since there are 5 cases on day t = 0, The formula for the number of cases of b.

  13. 13. ENVIRONMENTAL SCIENCE: Consumption of Natural Resources – World consumption of Silver is running at a rate of 20 e 0.02t thousand metric tons per year, where t is measured in years and t = 0 corresponds to 2008. a. Find a formula for the total amount of silver that will be consumed within t years of 2008. b. When will the known world resources of 570 thousand metric tons of silver be exhausted? a. To find the total amount of silver consumed, integrate the rate. Since there are 0 tons in year 2008 where t = 0, The formula for the silver used since 2008 is Continued

  14. b. To find the value of t that exhausts the 570 thousand metric tons, solve Thus, the world supply will be exhausted in 2031 (23 years from 2008).

  15. GENERAL: Cost of Maintaining a Home – The cost of maintaining a home generally increases as the home becomes older. Suppose that the rate of cost in dollars per year, for a home that is x years old is 200 e 0.4x. • Find a formula for the total maintenance cost during the first x years. Total maintenance should be 0 at t = 0. • Use that formula to find the total maintenance during the first 5 years. a. To find a formula for the total maintenance cost during the first x years, we integrate the rate of cost, r(x) = 200e0.04x(dollars per year). Since the total maintenance cost should be zero at x = 0, we can find C by evaluating M(0). The formula for the total maintenance cost during the first x years is b. Evaluate M(5) to find the total maintenance cost during the first 5 years.

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