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Basic Logarithmic and Exponential Integrals

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.

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Basic Logarithmic and Exponential Integrals

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  1. 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 ofwhen n = -1

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

  5. Integrating ex • 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 thetemp 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

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