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Integral Form of the Definition of Natural Logarithm ln(x)

This is an applet to explore the definition of the natural logarithm ln(x).

definition of natural logarithm

The integral is computed numerically using Simpson's rule.

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TUTORIAL 1 - click on the button above "click here to start" and MAXIMIZE the window obtained.

2 - The applet is started with x=1, ln(x) is given by the area from x=1 to x=1 which gives zero.

3 - Use the slider to change the coordinate x to 2. Click on reset and increase n which is the number of sampling points (see Simpson' rule) of the function from x=1 to x=2. Top left the area is an approximation to the integral. Check that it gives you a good approximation to ln(2). Compare the value obtained for ln(2) with the one given by your calculator.

4 - Repeat the experiment for different values of x.

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