Area Between Curves

The area between curves can be computed by performing the appropriate subtraction of the two expressions and integrating between limits. Suppose you want to find the area between the two parabolas shown below and in the figure.

Figure of Two Parabolas

First you must find the points of intersection of the two parabolas to determine the limits of integration. Then integrate the difference of the two functions between the points of intersection.

Solution to area is 108

If the two functions should cross over one another, changing places with which has greater magnitude, then the area will be determined as negative for that part of the integration unless you use the absolute value of the difference or compute the sum of of two different integrals.