http://www.ck12.org Chapter 1. Functions, Limits, and Continuity
We will use a variation of this covering of the region with quadrilaterals to get better approximations. We will do so
by dividing thex−interval fromx=0 tox=1 into equal sub-intervals. Let’s start by using four such subintervals
as indicated:
We now will construct four rectangles that will serve as the basis for our approximation of the area. The subintervals
will serve as the width of the rectangles. We will take the length of each rectangle to be the maximum value of the
function in the subinterval. Hence we get the following figure: