An improper integral with limit is an integral where one or both limits of integration are infinite or where the integrand is undefined at one or more points within the interval of integration.
An improper integral with limit differs from a regular integral in that it involves limits of integration that are not finite numbers and may require special techniques to evaluate.
Some common examples of improper integrals with limit include integrals with infinite limits of integration, integrals with discontinuous integrands, and integrals with unbounded integrands.
To determine if an improper integral with limit converges or diverges, you can use various techniques such as the comparison test, the limit comparison test, or the ratio test. If the limit of the integral exists and is a finite number, then the integral converges. If the limit does not exist or is infinite, then the integral diverges.
Yes, improper integrals with limit have various applications in physics, engineering, and economics, such as calculating the area under a curve that represents a continuous function with infinite limits, finding the center of mass of an object with variable density, and determining the total revenue from a continuous demand function.