A standard application of integration is to find the area between two curves.[br][br]The integration unit is the top function minus the bottom function.[br][br]The basic integral is [br][br][math]\int_{LeftEnd}^{RightEnd}\left(TopCurve-BottomCurve\right)dx[/math] [br][br]It should be noted that if top and bottom, or left and right, are reversed, the area is negative.

It is always good to start with a problem where we can find the answer without using integration.[br][list][*]A rectangle, Top(x)=4, Bottom(x)=1, Left = -2, Right =3[/*][*]A triangle, Top(x)=x, Bottom(x)=-1, Left = -1, Right =3[/*][*]A circle, Top(x)=sqrt(4-x^2), Bottom(x)=-sqrt(4-x^2), Left=-2, Right=2[/*][/list][br]One can then look are areas we cannot compute with simple geometry.[br][list][*]Bottom(x)=x^2, Top(x)=4, Left=-2, Right=2[/*][*]Bottom(x)=x^2, Top(x)=x+2, Left=-1, Right=2[/*][/list][br]One should also look at cases where the "top" and "bottom" curves cross.