http://www.ck12.org Chapter 4. Integration
4.3 The Area Problem
Learning Objectives
- Use sigma notation to evaluate sums of rectangular areas
- Find limits of upper and lower sums
- Use the limit definition of area to solve problems
Introduction
In The Lesson, The Calculus we introduced the area problem that we consider in integral calculus. The basic problem
was this:f(x) =x^2.
Suppose we are interested in finding the area between thex−axis and the curve off(x) =x^2 ,fromx=0 tox= 1.
We approximated the area by constructing four rectangles, with the height of each rectangle equal to the maximum
value of the function in the sub-interval.