5.6 Integration by Substitution Method (U-substitution) Thurs Feb 20

1. 5.6 Integration by Substitution Method (U-substitution)Thurs Feb 20 Do Now Find the derivative of

2. HW Review: p.326

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 #1-89 EOO

16. 5.6 U-Substitution Review / PracticeFri Feb 21 • Do Now • Evaluate the integrals • 1) • 2)

17. HW Review: p.333 1-89

18. Practice • Worksheet if time

19. Closure • Evaluate the integral • HW: p.333 #1-89 AOO

20. 5.6 Substitution MethodMon Feb 24 • Evaluate the integral using substitution

21. HW Review: p.333 1-89

22. Practice • Worksheet

23. Closure • When do we use substitution when integrating? How does it work? What about with definite integrals? • HW: none