Week 11: Area between curves

To find the area between two curves defined by functions, integrate the difference of the functions. If the graphs of the functions cross, or if the region is complex, use the absolute value of the difference of the functions. In general, two graphs y=f(x) and y=g(x) may cross. Sometimes f(x) may be larger and sometimes g(x) may be larger. In order to find the area enclosed by the curves, we can find where f(x) is larger, and where g(x) is larger, and then take the appropriate integrals of f(x)−g(x) or g(x)−f(x) respectively.Finally, unlike the area under a curve that we looked at in the previous chapter the area between two curves will always be positive. If we get a negative number or zero we can be sure that we've made a mistake somewhere and will need to go back and find it.