MA101 Study Guide - Final Guide: Antiderivative
Document Summary
Ma101 lab report 6 - substitution rule continued. 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. Let u = 1 + x2, then x2 = u 1 and du = 2xdx du = xdx. Example 2: sin x (6 + 2 cos x)3 dx. sin x (6 + 2 cos x)3 dx. 2 (64 1024) u3/2(cid:19) + c = Let u = 6 + 2 cos x.
