Chapter 5 Introduction to Integrals and Left End-point Method

We gave various examples of formulas for areas for geometric shapes, but how would you find the area under a graph? At every point the graph is changing, and there are infinite points.

One way we estimate the area under a graph is by drawing rectangles under the curve. In this way we can find an estimate less than the area:

Our estimate is the sum of the area of all of the rectangles under the curve. Notice that the rectangles do not include all of the area under the curve. Also notice that the height of each rectangle is determined by the top left endpoint of the rectangle. In words that might seem confusing, but just look at the picture below.

As you can see

Where the

Rectangle’s top

Left endpoint

Intersects the curve is

The height of the

Rectangle.