In this foldable, the natural logarithm function is defined as the area under the f(t) = 1/t curve from 1 to x. The students then discuss for what x’s ln x is +, -, or 0 based on the integral and the area under f(t). This definition reinforces the students understanding of a function defined as an integral and will eventually lead to finding the derivative of ln x.
All my foldables are self-guided which allow the students to start the foldable in class for about 10 to 15 minutes then complete the AP style examples at home. This foldable can be used alone or glued into an Interactive Notebook the size of a 9½ by 7½ composition book. Hope this is helpful. Enjoy!
This is the first foldable for Ch. 5 in our calculus textbook on transcendental functions thus the numbering 5-1. You can find other foldables related to the transcendental function chapter at
Calculus Foldable 5-2: Integration Strategies with Natural Log as Antiderivative
Calculus Foldable 5-3: Inverse Trig Review for Calculus
Calculus Foldable 5-4: Exponential and Inverse Trig Derivatives and Integrals
Table of Contents for the transcendental function chapter in my Interactive Notebook:
Calculus Interactive Notebook 5: Transcendental Functions
Integral Definition of Natural Logarithm © 2018 by Fan’s Math