The Natural Log Function: Integration Lesson 5.7

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

Try It Out Consider these . . .

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

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

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

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

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

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