Area under a Function Graph
Text Integrals are interpreted geometrically as the area under a function graph.
Specifically, for some variable x, a function f(x), and constants a and b, the integral
∫_{a}^{b}f(x)dx
is interpreted as the area between the xaxis and portions of the graph of f(x) for which y > 0 minus the area between the xaxis and portions of the graph of f(x) for which y < 0.
Demos
Area under a Function Graph
 
This demo how the area under a function graph can be approximated by rectangles. You can view either the right or the leftsided rectangles by clicking the appropriate checkboxes in the control panel.

Exercises Use the demo to estimate the values of the following integrals:
 ∫_{0}^{1}1dx
 ∫_{0}^{1}xdx
 ∫_{1}^{1}x^{2}dx
 ∫_{0}^{1}1dx
 ∫_{1}^{1}x^{3}dx
