Basic Logarithmic and Exponential Integrals Lesson 9.2

2 Review Recall the exception for the general power formula Recall also from chapter 8 that We will use this and the fact that the integral is the inverse operation of the derivative

3 Filling in the Gap Since then  Note the absolute value requirement since we cannot take ln u for u < 0 Thus we now have a way to take the integral of when n = -1

4 Try It Out! Consider What is the u? What is the du? Rewrite, integrate, un-substitute

5 Integrating e x Recall derivative of exponential Again, use this to determine integral For bases other than e

6 Practice Try this one What is the u, the du? Rewrite, integrate, un-substitute

7 Area under the Curve What is the area bounded by y = 0, x = 0, y = e –x, and x = 4 ? What about volume of region rotated about either x-axis or y-axis?

8 Application If x mg of a drug is given, the rate of change in a person's temp in °F with respect to dosage is A dosage of 1 mg raises the temp 2.4°F.  What is the function that gives total change in body temperature? We are given T'(x), we seek T(x)

9 Application Take the indefinite integral of the T'(x) Use the fact of the specified dosage and temp change to determine the value of C + C

10 Assignment Lesson 9.2 Page 362 Exercises 1 – 33 odd