1. Intergration and U-Substitution
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4-A

2. Basic Integration Rules
Remember derivatives and integrals are inverse operations
Hence: antiderivative
The definite integral can be thought of as the area between a and b and between the curve of f(x) and the x-axis

3. U-substitution
Integral form of the chain rule (function times its derivative)
Where u is a function of x

4. 1) Find

5. Integration by Recognition
x form u form (Reverse Chain Rule)
Power Rule:
Trig Rules:

6. 2) Find

7. 3) Find

8. 4) Find

9. Definite Integral Substitution
Perform a complete change of variables
Including the limits of integration

10. 5) Find

11. 6) If 0 < k < π then

12. 7) find

13. 8) find

14. 9) find

15. 10) Suppose f is a continuous function and

16. Home Work U-substitution worksheet
Use a section header for each of the topics, so there is a clear transition to the audience.
U-substitution worksheet
And page 306 #13,19, 27, 67, 68, 69, 70 & 71