1. 5.6 Integration by Substitution Method (U-substitution) Thurs Dec 3 Do Now Find the derivative of

2. HW Review

3. Reverse Chain Rule Looking at the 2 Do Now problems, we can say Notice how 2 factors integrate into one

4. Substitution Method If F’(x) = f(x), then

5. Integration by Substitution (U-Substitution) 1) Choose an expression for u – Expressions that are “inside” another function 2) Compute 3) Replace all x terms in the original integrand so there are only u’s 4) Evaluate the resulting (u) integral 5) Replace u after integration

6. Expressions for U-substitution Under an exponent Inside a function (trig, exponential, ln) In the denominator The factor in a product with the higher exponent Remember: you want to choose a U expression whose derivative will allow you to substitute the remainder of the integrand!

7. Ex1 Evaluate

8. Ex 2 – Multiplying du by constant Evaluate

9. Ex 3 – u in the denominator Evaluate

10. Ex 4 - Trig Evaluate

11. Ex 5 – Integrating tangent Evaluate

12. Ex 6 – 2 step Substitution Evaluate

13. Substitution and Definite Integrals When using u-substitution with definite integrals you have 2 options – Plug x back in and evaluate the bounds that way – Change the x bounds into u bounds and evaluate in terms of u

14. Ex Evaluate

15. Closure Evaluate the integral HW: p.333-335 #9 13 20 31 43 53 59 67 69 74 81 89 95

16. 5.6 U-Substitution Review / Practice Wed Feb 11 Do Now Evaluate the integrals 1) 2)