00:06
The definite integral will equal the area of the region where the function is positive minus the area of the region when the function is negative.
00:22
So the definite integral gives you the net area.
00:26
The area where the function was positive minus the area where the function was negative.
00:32
The only time the definite integral will equal the area is when you don't have the function being negative, the function, the curve being underneath the x -axis.
00:46
For example, if instead of integrating from a to b, if i was integrating from a to d, okay, if we're looking at the definite integral from a to d of f of x, then since f of x is a, positive on the interval from a to d, this is when the definite integral, okay, will be the area under the curve, the area between the curve and the x axis.
01:17
Okay, so the definite integral equals the area between the function and the x axis only when the function is positive...