1. Integration Techniques
AB & BC Techniques
By: Gina Chang, Umesh Radhakrishnan, and Hunter Hammack

2. “Father of Integration”- Gottfried Wilhelm Leibniz and Isaac Newton
HISTORY LESSON!
“Father of Integration”- Gottfried Wilhelm Leibniz and Isaac Newton
Gottfried Wilhelm Leibniz
Isaac Newton

3. Classwork/ Homework Classwork Homework AB PACKET AB PACKET
MC MC FRQ 20-23
BC PACKET BC PACKET
MC MC 1-9
FRQs 21-23

4. General Rules for Integration
DON’T FORGET COOKIES!!! :D
General Rule for Integration:

7. Note Card #29: Improper Integrals

8. Card #30: Power Rule for Integration

9. Card #31: Trig Rules for Integration
SIN
-COS
COS
-SIN

10. Card #32: Inverse Trig Rules for Integration

11. Card #33: Exponential and Log Rules for Integration
Helpful Log Properties!!

12. Card #34: U-Substitution
U-Substitution Steps:
Choose a new variable u
Determine the value dx
Make the substitution
Integrate resulting Integral
Return to the initial variable x or change bounds using u.

13. Card #35: Integration using Completing the Square
How to Integrate this
Quadratic Equation in Standard Form: ax2 + bx + c = 0
Make sure a = 1. If not, factor the coefficient out, and take it out of the integral (it is a constant)
Take B, divide it by 2, and square it. Let's say this value becomes c₂. After this step, your denominator should be x2 + bx + c₂ + c
Factor the first 3 terms, and make c, the square root of c, squared. After this step, your denominator should be [(x+k)^2]+(√c)^2
Use the tan inverse integral rule **don’t forget your cookies :)
**Make sure you do a u-sub on the term with the x in it. 1

14. Card #36: Integration by Parts
ULTRAVIOLET VOODOO(DU)!
Steps: 1. Choose U using ILATE
2. Solve for missing parts of the formula, du= derivative of U, V=integral of dv
3. Sub all parts into the formula
4. Integrate (repeat if necessary)
ILATE
Inverse
Logs
U = (Choose U using ILATE)
V = Integral of dv
Du = Derivative of U
Dv = The unused expression

15. Card #37: Integrating with Partial Fractions
Steps to Partial Fraction integration:
Check to see if u-sub or inverse trig is possible
Check if denominator is factorable
Factor the denominator and split the function into two separate fractions
Solve for A and B
Integrate both accordingly

16. Card #38: Integrating Absolute Value Functions
Graph the Absolute Value Function
Find the area under the curve, using geometric formulas. For example, Triangle and Trapezoidal Area
***Make sure you find the area, under the function, on the interval they give you
***When the area is under the x-axis, the area is negative
How to graph an Absolute Value Function

17. Card #39: Limit Definition of a Definite Integral
Δx = (b-a)/n **a and b are the limits of the integral
Xᵢ = a + (Δx *i)

18. Card #40: Fundamental Theorem of Calculus Part 1 (Evaluating a Definite Integral)
If F’(t) is continuous on [a,b], and F(t) is the antiderivative of F’(t) on [a,b], then...

19. Card #41: Fundamental Theorem of Calculus Part 2 (Derivative of an Integral)
Make sure the derivative variable matches with the integral variable
If #1 passes, just plug the integral variable in for all variables found in the function
If #1 doesn’t pass, put the integral variable in for all variables found in the function, and multiply everything by the derivative of the integral variable :)

20. Quizizz