Improper integrals
A definite integral is an integral between two finite points a and b:
We normally expect f to be continuous and bounded over the interval [a, b].
It is sometimes possible to break these conditions. Integrals that break these conditions are called improper integrals, but in some cases it is quite possible to calculate the area under the curve. Here are three examples:
The first is:
This integral extends to infinity, but as x tends to infinity, the function tends to zero, and we will show that the area under the curve converges to a finite value.
The second is:
The final integral is:
This integral goes from minus infinity to infinity. As x tends to infinity in either direction, the function tends to zero, and again we will show that the area under the curve converges to a finite value.
