# How do I find a natural log without a calculator?

##### 1 Answer

You can approximate

#### Explanation:

For example, to approximate

#(x_n, 0)# ,#(x_n, 1/x_n)# ,#(x_(n+1), 0)# ,#(x_(n+1), 1/(x_(n+1)))#

If we use strips of width

If you add these, you find:

#3/4+5/12+7/24+9/40+11/60+13/84 ~~ 2.02#

If we use strips of width

Then the total area is:

Actually

Simpson's rule approximates the area under a curve using a quadratic approximation. For a given

#h/3(f(x_0) + 4f(x_0+h) + f(x_0+2h))#

Try improving the approximation using Simpson's rule, using

#h/3(25/6+73/30+145/84+241/180+361/330+505/546)~~1.947#

That's somewhat better.