5.5 The Substitution Rule

First Review Chain Rule for Derivatives

Examples:

The Substitution Rule

If u = g(x) is a differentiable function whose range is an interval I, and f is continuous on I, then

Examples:

(?2 methods)

The Substitution Rule for Definite Integrals

If g' is continuous on [a,b] and f is continuous on the range of u = g(x), then

Note: There are two methods for using substitution on definite integrals. The rule above, gives only one of them. Alternatively, the integral can be evaluate in terms of the variable x, and the original a and b used for evaluating.

Evaluate the definite integral, if it exists.

#36 #40

#46

Symmetry - Integrals of Symmetric Functions

Suppose f is continuous on [-a,a],

a) If f is even [f(-x) = f(x)], then

b) If f is odd [f(-x) = -f(x)], then

Assignment: 5.5, pg. 338; 5-13 odd,17-29 odd, 35-49 odd, *57, *59

Chapter Review; Pg 341; 1, 3, 4, 5, 7, 9-19 odd, *21, 23-235 odd, 44, 45, 49, *52, *54