MATH 3B Midterm: Math 3B Exam 3
Document Summary
Rules for derivatives easily transform into rules for integration. The most important rule for derivatives is the chain rule, i. e. , A rational function is one of the form p (x) We have already en- countered several of these types of functions for inte- grating. For example we have the following: d dx(cid:0)f (g(x))(cid:1) = f (g(x))g (x). Z f(cid:0)g(x)(cid:1)g (x) dx = z f (u) du, where u = g(x). This is used in many problems involving integration because it can help rewrite the integral in a simpler form. So after the substitution we might see how to proceed and then we can solve the integral and at the end resubstitute back to get our answer in terms of x. One indication that we should use use substitution is to look for a function inside of a function. If we are dealing with a de nite integral we can do one of two things.
