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

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.

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