## Sunday, May 22, 2011

### Area Between Two Curves

Let say we have 2 functions as given in the graph below:

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If we want to find the area between the two functions from x = a to x = b, we integrate
a) f(x) - g(x) from x = a to x = b if f(x) > g(x)
$\inline \int_{a}^{b}f(x)-g(x)\; dx$;

b) g(x) - f(x) from x = a to x = b if g(x) > f(x)
$\inline \int_{a}^{b}g(x)-f(x)\; dx$.

e.g. Slide the values of a and b to a = -5 & b = 6. The area found is 125.59 (positive). Take note that I take the integration of f(x) - g(x) to find the area falls between the two functions. Now, if we change the values of a and b to a = 9 & b = 12, we get -26.15 for the area. This is because we didn't change the integral to g(x) - f(x), and g(x) > f(x) for 9 < x < 12.

Betty, Created with GeoGebra