Basic Logarithmic and Exponential Integrals Lesson 9.2

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

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

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

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

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

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?

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)

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

Assignment Lesson 9.2 Page 362 Exercises 1 – 33 odd