Basic Logarithmic and Exponential Integrals Lesson 9 2

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 2

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 3

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

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

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

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? 7

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) 8

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

Assignment • Lesson 9. 2 • Page 362 • Exercises 1 – 33 odd 10