1. SECTION 6.2 Integration by Substitution

2. U-SUBSTITUTION

3. USING THE SUBSTITUTION METHOD

4. EXAMPLE

5. WHAT IF THERE IS A CONSTANT LEFT OVER?

6. METHOD 2: “BEACH BOYS”

7. ADDITIONAL EXAMPLES

8. USING TRIG IDENTITIES

9. DO-NOW: HOMEWORK QUIZ  Suppose that a point moves along some unknown curve y = f(x) in the xy-plane in such a way that at each point (x, y) on the curve, the tangent line has a slope x 2. Find an equation for the curve given that it passes through the point (2, 1).

10. U-SUBSTITUTION IN DEFINITE INTEGRALS  Two methods for calculating the definite integral:  1. Perform the u-substitution, integrate, substitute back in for u, and evaluate at the given limits of integration.  2. Perform the u-substitution, integrate, change the limits of integration from x to u, and evaluate the function of u at the new limits of integration.

11. EXAMPLE

12. ADDITIONAL EXAMPLES

13. AP MC PRACTICE

15. MORE AP MC PRACTICE

16. DO-NOW: HOMEWORK QUIZ

17. SEPARABLE DIFFERENTIAL EQUATIONS

18. EXAMPLES