For improper integrals, it is important to remember that an integral from some point (or negative infinity) to infinity cannot be evaluated using standard integration techniques. The reason that this happens is when evaluating an integral using the Fundamental Theorem of Calculus, we evaluate the integral then plug in the endpoints. however, this is not possible when considering infinity because if we anted to evaluate an integral with infinity using the Fundamental Theorem of Calculus, , we would have to evaluate the integral at infinity. This implies that infinity is a number, but we know that infinity is not a number. because of these reasons, we must use a limit to send the number to infinity.

Integrals with infinity

Assuming that each integral is continuous along its domain