The substitution Rule

1. The substitution Rule ‘U-Substitution’ Section 5.5

2. Antidifferentiation of a composite function • Let f and g be functions such that f(g(x)) and g’(x) are continuous on an interval I. If F is an antiderivative of f on I, then

3. Guidelines for integration by substitution • Choose a substitution u=g(x) (inner part) • Compute du=g’(x)dx • Rewrite the integral in terms of the variable u • Evaluate the resulting integral in terms of u • Replace u by g(x) to obtain antiderivative

4. Examples

5. Ex. Definite Integral (2 ways)

6. 2nd Way

7. Extra Variable

8. Trig!

9. U-Sub – More Practice