Simply put, u-Substitution is reverse of chain rule. Recall that below is the chain rule. u-Substitution is following. To find from, use following procedure. 1.Let and (think of it as manipulation of.) 2.Then turns into simple. 3.Evaluate this simpler integral, and then substitute back g(x) into u as following., where f is derivative of F. u-Substitution for Indefinite Integral Lesson: P.306, where F is antiderivative of f.
There are two ways to evaluate definite integral using the u-Substitution. Method 1: To evaluate, ignore a and b to find the indefinite integral. Then use values of a and b to calculate. No need to worry about C, because it is cancelled in definite integral. Method 2: To change in terms of, change values of a and b into and so that we can write. Then evaluate. u-Substitution for Definite Integral Lesson: P.310 - 311