MA101 Study Guide - Final Guide: Antiderivative
Document Summary
Ma101 lab report 7 - substitution rule, integration by parts. Used to express the integrand in a form where the general antiderivative is known. We try to make a substitution, say u = g(x), where both g(x) and g (x) are factors in the integrand. = z f (u)du let u = g(x), then du = g (x)dx. Any limits of integration must be changed to reflect the change of variable; that is, Z b a f (g (x)) g (x) dx = z g(b) g(a) the original variable. For inde nite integrals, the nal answer must be expressed as a function of. We have evaluated integrals using the method of substitution. When integration by substitution isn"t successful, a second technique to try is integration by parts: Z f (x) g (x) dx = f (x) g (x) z f (x) g (x) dx or. Z u dv = uv z v du .
