The Natural Log Function: Integration

The Natural Log Function: Integration

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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