# MTH 252 Integral Calculus Chapter 6 – Integration Section 6.9 – Logarithmic Functions from the Integral Point of View Copyright © 2005 by Ron Wallace,

## Presentation on theme: "MTH 252 Integral Calculus Chapter 6 – Integration Section 6.9 – Logarithmic Functions from the Integral Point of View Copyright © 2005 by Ron Wallace,"— Presentation transcript:

MTH 252 Integral Calculus Chapter 6 – Integration Section 6.9 – Logarithmic Functions from the Integral Point of View Copyright © 2005 by Ron Wallace, all rights reserved.

The Area Function 1x A(x) > 0 1x A(x) < 0 Domain?Range? Derivative? FTC, Pt. II What function has these characteristics?

The Natural Logarithm Function Properties of Logarithms Proof: Functions w/ same derivative differ by a constant. Let x = b

The Natural Logarithm Function Properties of Logarithms Let a=1/b in above. a/b = a(1/b), use above 3 Cases: r pos. integer r neg. integer r rational

The Natural Exponential Function Derivative of inverse rule!

Download ppt "MTH 252 Integral Calculus Chapter 6 – Integration Section 6.9 – Logarithmic Functions from the Integral Point of View Copyright © 2005 by Ron Wallace,"

Similar presentations