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

“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

Classwork/ Homework Classwork Homework AB PACKET AB PACKET MC 1-12 MC 13-19 FRQ 20-23 BC PACKET BC PACKET MC 1-10 MC 1-9 FRQs 21-23

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

Note Card #29: Improper Integrals

Card #30: Power Rule for Integration

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

Card #32: Inverse Trig Rules for Integration

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

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.

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

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

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

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

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)

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...

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 :)

Quizizz https://quizizz.com/join/quiz/5ca6bfac740aa1001a3ad19b/start