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The Natural Log Function: Integration

Learn how to find the area under the curve using long division before integrating and the log rule for integration. Explore the use of change of variables and integrals of trig functions. Complete assignment exercises to practice these concepts.

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The Natural Log Function: Integration

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  1. The Natural Log Function: Integration Lesson 5.7

  2. Log Rule for Integration • Because • Then we know that • And in general, when u is a differentiable function in x:

  3. Try It Out • Consider these . . .

  4. Finding Area • Given • Determine the area under the curve on the interval [2, 4]

  5. Using Long Division Before Integrating • Use of the log rule is often in disguised form • Do the division on this integrand and alter it's appearance

  6. Using Long Division Before Integrating • Calculator also can be used • Now take the integral

  7. Change of Variables • Consider • Then u = x – 1 and du = dx • But x = u + 1 and x – 2 = u – 1 • So we have • Finish the integration

  8. Integrals of Trig Functions • Note the table of integrals, pg 357 • Use these to do integrals involving trig functions

  9. Assignment • Assignment 5.7 • Page 358 • Exercises 1 – 37 odd 69, 71, 73

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