1. Integration Techniques
Dominic, Dylan, James

2. Power Rule for the Indefinite Integral
-Don’t forget cookies!

3. Power Rule for the Indefinite Integral
-Don’t forget absolute value!

4. Indefinite Integral for e and constants
-Where b=constant

5. Integration Formulas for Trig Functions

6. Try it yourself! 1. 2. 3.

7. Particular Solutions +C is general solution
If given initial condition, we can find particular solution
Find f(x) by integrating
Insert initial condition to find C
Plug C into original f(x)

8. Try it yourself! 4.
Find f(x)

9. The Definite Integral
-Bounded by a and b

10. Example

11. Net Area
Area under x-axis is considered negative area -

12. Properties of the Integral

13. Properties cont.

14. Properties of Even and Odd Functions

15. Fundamental Theorem of Calculus, part 1
If f is continuous on [a,b] and F is any antiderivative of f on [a,b] then

16. Try it yourself! 5.

17. Average Value
Integral/Interval

18. Try it yourself! 6.

19. Fundamental Theorem of Calculus, part 2

20. Examples

21. Examples cont.

23. Try it yourself! 7.

24. Try it yourself!
8. Find LRAM using 5 rectangles

27. Trapezoidal Rule

28. Displacement vs Total Distance

29. U-SUB Opposite of Chain Rule
Variable of integration must match variable in expression
Substitute value of u back into problem

30. Example

31. Try it yourself! 9.

32. Additional Information
Barron’s AP Review Books
College Board FRQs
Unit 4 Tests/Quizzes
Dominic - Presentation
Dylan - Quizizz
James - 5n1