## Thursday, May 24, 2012

### Natural Logarithm

Some book authors define the natural logarithm function, ln (x) as

$ln(x)=\int_{1}^{x}\frac{1}{t}dt,\; \; x>0$.

If we take a look at the graphs below, the red curve represents the graph of $y=\frac{1}{x}$, and the dark green curve represents the graph of $y=ln(x)$. The purple region falls below the red curve is bounded between x = h and 1, while the blue region is bounded between x = 1 and k.

Now scroll the value of k, do you notice that point K moves according to the k value? The y-coordinate of point K is the area of the blue region. Same concept applies to the value of h and point H. Here comes the question, do you know how to get negative y-coordinate for point H?

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Betty, Created with GeoGebra