The Natural Logarithmic Function: Integration (5.2)

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Presentation transcript:

The Natural Logarithmic Function: Integration (5.2) December 7th, 2016

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. b. c.

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

*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.

Ex. 3: Solve the differential equation .

II. Integrals of the Trigonometric Functions

Ex. 4: Find .

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