I What Defines an Improper Integral?

[NihalRi]

I find it easy to picture bounder integrals because they are the area under the graph but when it is unbounded what is it exactly. If we evaluate it we find the equation of a many possible graphs where the derivative is the function that was originally in the integral. How did we get from that to area?

 

[chiro]

Hey NihalRi.

For improper integrals we look at limits and require that the integral have some sort of convergence.

 

[Rajesh Bhuria]

While evaluating $\int\limits^b_a f(x)dx$ there was an assumption that
(1) f does not have an infinite discontinuity in $[a, b]$
(2) The integral interval $[a,b]$ is not infinite i.e, both a and b are finite values. (Edited by mentor)
If either of the above 2 condition is violated we say that the integral $\int\limits^b_a f(x)dx$ is an improper integral.