The Substitution Method | Calculus Course: Theory Part 107

How can changing a variable make an integral easier? This theory lesson is part of Calculus, Full Course with Theory and Practice. Understand substitution as the reverse chain rule through linked graphs and carefully explained examples. Learn how to choose the new variable, account for every factor, substitute back, and change definite-integral bounds. The lesson also explains reversed bounds, substitutions that turn around, inverse branches, and interval and regularity conditions. Assumed background: functions, the chain rule, elementary antiderivatives, and the basic meaning of a definite integral. Chapters 00:00 Substitution and the reverse chain rule 01:36 Change of variable 03:28 Indefinite integrals and back-substitution 07:24 Definite-integral bounds 09:18 Direction and substitutions that turn around 11:13 Domains and interval conditions 13:20 Inverse branches and choosing a substitution