How do i figure out if integrals are improper or not and how do i know which limit is undefined?

Improper integrals can take many forms. The first step when dealing with a potentially improper integral is to test the limits of the integral i.e. a and b. If these are at infinity/negative infinity, or the points are undefined at that value. You will have an improper integral. However, that ma not be the end of it. You will also have to quickly check that the curve is continuous over the integration, meaning that there are no asymptotes or undefined points midway through your integral. If there is such a point, the integral will need to be split into two - one integral for each side of the undefined point. Now we can actually solve our integral. Improper integrals can either be convergent or divergent - basically meaning whether the integral works or not. Convergent integrals will give us an answer whereas divergent ones will not. We should replace our undefined limit with t and create a limit. That limit will be t tends to x, where x is the undefined point. From there we perform our integration and solve.