*use a finite approximation to estimate the area under the graph of the given function on the stated interval *

*f(x)= 1/x between x=4 and x=5 using a lower sum with two rectangle of equal width*

Two rectangles of equal width means that we have three points, x0 = 4, x1 = 4.5 and x2 = 5.

Using lower sums means that we take the lower of the two f(x)-values on each interval. i.e.

1st rectangle: width = 0.5, height = f(x1) = f(4.5) = 0.2222, Area = A1 = 0.5 * 0.2222 = 0.1111

2nd rectangle: width = 0.5, height = f(x2) = f(5) = 0.2, Area = A2 = 0.5 * 0.2 = 0.1

**Total Area is A = A1 + A2 = 0.1111 + 0.1 = 0.2111**

The exact value, using integral calculus, is 0.2231, which confirms that we have a lower sum.