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The Natural Logarithmic Function: Integration (5.2)

The Natural Logarithmic Function: Integration (5.2). February 26th, 2013. I. Log Rule for Integration. Thm. 5.5: Log Rule for Integration: Let u be a differentiable function of x. 1. 2. Ex. 1: Find each indefinite integral. a. b. c.

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The Natural Logarithmic Function: Integration (5.2)

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  1. The Natural Logarithmic Function: Integration (5.2) • February 26th, 2013

  2. I. Log Rule for Integration Thm. 5.5: Log Rule for Integration: Let u be a differentiable function of x. 1. 2.

  3. Ex. 1: Find each indefinite integral. a. b. c.

  4. Ex. 2: Find the area of the region bounded by the graphs of the equations , x=1, x=4, and y=0.

  5. Ex. 3: Find .

  6. Ex. 4: Find .

  7. *Guidelines for Integration 1. Know the 12 basic integration formulas you’ve already learned: the power rule, the log rule, and the 10 trigonometric rules. 2. Try to recognize which of those formulas best matches the integrand, and choose u accordingly. 3. If nothing fits, try to manipulate the integrand using algebra or trigonometric identities.

  8. Ex. 5: Solve the differential equation .

  9. II. Integrals of the Trigonometric Functions

  10. Ex. 6: Find .

  11. Ex. 7: Find the average value of f(x)=csc x on the interval .

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