How To: Use definite integrals to find the area of curves

Brightstorm explains how to use definite integrals to find area. There are two basic area problems: one in which the area lies between the function and the x-axis, and one where the area lies between the two functions. In the first case, if the curve lies above the x-axis for x=a to x=b, the definite integral returns the area. If it lies below the x-axis for x=a to x=b, then the definite integral returns a negative area. In the second case, we assume that f(x) is the higher curve and g(x) is the lower one. The area then is the area under y=f(x) minus the area under y=g(x). When taken as definite integrals, those can be combined as the integral from x=a to x=b of f(x)-g(x). This simplifies the problem to a single integral of the difference of the two functions.