What is L’Hôpital’s rule in integration?

L'Hôpital's rule is a mathematical technique used to evaluate limits of indeterminate forms that involve functions that approach zero or infinity. It is commonly used in calculus to evaluate limits of functions that are in the form of 0/0 or ∞/∞. The rule states that if the limit of the ratio of two functions f(x) and g(x) as x approaches a certain value is in the form of 0/0 or ∞/∞, then the limit of the ratio of their derivatives f'(x) and g'(x) will be the same as the original limit. This rule can be applied repeatedly until a determinate form is obtained, allowing for the evaluation of the limit.

L'Hôpital's rule does not apply to integration. L'Hôpital's rule is a method for evaluating indeterminate limits of the form 0/0 or ∞/∞ for functions of a single variable. In contrast, integration is a process of finding the area under the curve of a function, and does not involve evaluating limits.