Area Below The Curve

When we wish to find the area falls between function f(x) with x-axis for a < x < b, we integrate f(x) with respect to x from x = a till x = b, and we write it as . Let's take a look at the graph below:


Try to slide the values of a and b according to the suggested values below and look at the area found.

a) If a = 0, b = 7, f(x) is positive for 0 < x < 7, the area is 23.57 (positive).
b) If a = 7, b = 10, f(x) is negative for 7 < x < 10, the area is -6.9 (negative).
c) If a = 0, b = 10, f(x) is positive for 0 < x < 7 and is negative for 7 < x < 10, the "area" given is 16.67, which is the result of 23.57 + (-6.9), which means the "area" here is a SIGNED AREA.

What do you suggest if you wish to find the total area falls between f(x) and x-axis for 0 < x < 10?

Betty, Created with GeoGebra