September 10, 2009
No CommentsHow to Solve an Integration Problem by Parts
Description
Step-by-step tutorial of the integration by parts method. Several examples are provided in this video. Knowledge of integration by parts is required in calculus.
Overview
Very often, you will see an integral that is also a multiplication problem. There was such a thing as the product rule for derivatives, but what about for anti-derivatives? There is some sort of reverse product rule, and that is what integration by parts is. Sometimes it is also called u-substitution, but the term is misleading because substitution is something else. A basic integration by parts problem is set up like this:
You are allowed to choose which value is your u and which value is your dv. Choosing involves something called LIATE – Logarithmic, Inverse Trigonometric, Algebraic, Trigonometric, Exponential. Put this on a ladder scale, with L being first and E being last. Each term you are multiplying falls on one of the parts of this chart. The highest one will be your u, and the lower one will be your dv. Sometimes you will have to perform integration by parts more than once in a problem.
