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The Natural Logarithmic Function: Integration (5.2)

Learn how to integrate using the log rule and apply it to find indefinite integrals and area under curves. Follow guidelines for integration and solve trigonometric functions. Understand integrals of trigonometric functions.

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The Natural Logarithmic Function: Integration (5.2)

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  1. December 5th, 2017 The Natural Logarithmic Function: Integration (5.2)

  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. *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.

  6. Ex. 3: Solve the differential equation .

  7. II. Integrals of the Trigonometric Functions

  8. Ex. 4: Find .

  9. Ex. 5: Find the average value of on the interval .

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