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Miss Battaglia AP Calculus

The Natural Logarithmic Function: Integration Objective: Use the Log Rule for Integration to integrate a rational function and integrate trig functions. Miss Battaglia AP Calculus. Log Rule for Integration. Let u be a differentiable function of x . 1. 2.

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Miss Battaglia AP Calculus

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  1. The Natural Logarithmic Function: IntegrationObjective: Use the Log Rule for Integration to integrate a rational function and integrate trig functions. Miss Battaglia AP Calculus

  2. Log Rule for Integration Let u be a differentiable function of x. 1. 2.

  3. Using the Log Rule for Integration

  4. Using the Log Rule with a Change of Variables Find

  5. Finding Area with the Log Rule Find the area of the region bounded by the graph of the x-axis, and the line x=3

  6. Recognizing Quotient Forms of the Log Rule a. b.

  7. Recognizing Quotient Forms of the Log Rule c. d.

  8. Using Long Division Before Integrating Find

  9. Change of Variables with the Log Rule Find

  10. Guidelines for Integration (p. 337) • Learn a basic list of integration formulas • Find an integration formula that resembles all or part of the integrand, and, by trial and error, find a choice of u that will make the integrand conform to the formula. • If you cannot find a u-substitution that works, try altering the integrand. You might try a trig identity, multiplication and division by the same quantity, addition and subtraction of the same quantity, or long division. Be creative. • If you have access to computer software that will find antiderivatives symbolically, use it.

  11. u-Substitution and the Log Rule Solve the differential equation

  12. Using a Trig Identity Find

  13. Derivation of the Secant Formula Find

  14. Integrals of the Six Basic Trig Functions

  15. Integrating Trig Functions Evaluate

  16. Find an Average Value Find the average value of f(x) = tanx on the interval

  17. Classwork/Homework • Read 5.2 Page 340 #1-25 odd, 22

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