9 9 1 1 5 5 6 6 7 7 + 5 5 + 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 3-2+1=? Advanced Placement Calculus BC Project Created by Tony Wen(Cheng-cheng.

Slides:



Advertisements
Similar presentations
Clicker Question 1 What is ? – A. 1 / (1 + x 2 ) + C – B. x / (1 + x 2 ) + C – C. sin( ) – D. (1 + x 2 ) + C – E. (1 + x 2 ) / x + C.
Advertisements

u-du: Integrating Composite Functions
3.3 Solving Multi-Step Equations. A multi-step equation requires more than two steps to solve. To solve a multi-step equation: you may have to simplify.
Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.
Example 1 Solve ax b c for x. Then use the solution to solve Solve a literal equation + = += 2x SOLUTION STEP 1 Solve ax b c for x. += ax b c Write.
EXAMPLE 4 Solve equations using nth roots Solve the equation. a. 4x 5 = 128 Divide each side by 4. x5x5 32= Take fifth root of each side. x=  32 5 Simplify.
Solve an equation with variables on both sides
Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =
4 step by step on solving linear equations
Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.
Standardized Test Practice
Algebraic Fractions and Forming Equations Learning Outcomes  Simplify algebraic fractions  Add, subtract, multiply and divide algebraic fractions  Solve.
Solve the equation -3v = -21 Multiply or Divide? 1.
Topic 1Topic 2Topic 3Topic 4Topic
Substitution Method: 1. Solve the following system of equations by substitution. Step 1 is already completed. Step 2:Substitute x+3 into 2 nd equation.
TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using.
Differential Equations BC CALCULUS. Differential Equations Defn: An equation that contains a derivative ( or a function and a derivative ) is called.
Derivation of the Quadratic Formula The following shows how the method of Completing the Square can be used to derive the Quadratic Formula. Start with.
Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =
13.2 Integration by Substitution. Let w be the inside function Write Do cross-multiply Back to the given integral and do the substitution Take the integral.
Day 5 Objective – Students should be able to: Find the y intercept when given the slope and a point on the line.
Table of Contents Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic.
Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.
Solving by Elimination Example 1: STEP 2: Look for opposite terms. STEP 1: Write both equations in Standard Form to line up like variables. STEP 5: Solve.
Section 5.3 Solving Systems of Equations Using the Elimination Method There are two methods to solve systems of equations: The Substitution Method The.
Solve an equation using addition EXAMPLE 2 Solve x – 12 = 3. Horizontal format Vertical format x– 12 = 3 Write original equation. x – 12 = 3 Add 12 to.
Example 1 Solving Two-Step Equations SOLUTION a. 12x2x + 5 = Write original equation. 112x2x + – = 15 – Subtract 1 from each side. (Subtraction property.
Solving Linear Equations Substitution. Find the common solution for the system y = 3x + 1 y = x + 5 There are 4 steps to this process Step 1:Substitute.
EXAMPLE 1 Solve a two-step equation Solve + 5 = 11. x 2 Write original equation. + 5 = x – 5 = x 2 11 – 5 Subtract 5 from each side. = x 2 6 Simplify.
Systems of Equations: Substitution
Use the substitution method
Solve Linear Systems by Substitution January 28, 2014 Pages
© by S-Squared, Inc. All Rights Reserved.
A.2 B.3 C.4 D.5 Refer to the figure. Find BC.. A.2 B.3 C.4 D.5 Refer to the figure. Find BC.
Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.
Notes 6.5, Date__________ (Substitution). To solve using Substitution: 1.Solve one equation for one variable (choose the variable with a coefficient of.
Solve a two-step equation by combining like terms EXAMPLE 2 Solve 7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide.
Ch. 9 Review AP Calculus. Test Topics -- INTEGRATION NO CALCULATOR!!!!
6-2 Solving Systems Using Substitution Hubarth Algebra.
1) Solve. -5t = 60 To get the variable by itself, which number needs to be moved? -5 To move the -5, you have to do the opposite operation. What operation.
Balancing Equations The student will be able to: solve equations using addition and subtraction.
Substitution Method: Solve the linear system. Y = 3x + 2 Equation 1 x + 2y=11 Equation 2.
Example: Solve the equation. Multiply both sides by 5. Simplify both sides. Add –3y to both sides. Simplify both sides. Add –30 to both sides. Simplify.
EXAMPLE 2 Rationalize denominators of fractions Simplify
Solve Systems of Equations by Elimination
Completing the Square 8
Solve a literal equation
Solve for variable 3x = 6 7x = -21
Solve an equation by multiplying by a reciprocal
Solve a quadratic equation
Solving Two-Step Equations
6-2 Solving Systems Using Substitution
Solving One-Step Equations
Solving Systems using Substitution
Bellwork1/26 Solve by Graphing: x + 2y = 7 x + y = 1.
Solving Systems of Equations by Elimination
Unit 4 Lesson 1: Completing the square
Objective The student will be able to:
Solve an equation by combining like terms
Solving Systems of Equation by Substitution
Solving Multi-Step Equations
Section 4.5A Calculus AP/Dual, Revised ©2019
Solving One and Two Step Equations
Solving One Step Equations
Work out (if you can, simplify your answer) 8 6.
Dividing Decimals Guided Notes
Solve equations using multiplication and division.
Objective The student will be able to:
Solving basic equations
Integration Techniques
Presentation transcript:

=? Advanced Placement Calculus BC Project Created by Tony Wen(Cheng-cheng Wen) Topic : Integration Date : December 01, 2007 Teacher: Ms. DelaCruz

1. k now the derivative of trigonometry and others 2. A nd knowing how to do the substitution 3. R emember to put a C at the end of your answer (This is the Most IMPORTANT) because if you dont put a c in the answer then

Find the answer to the following: Step 1: you separate the whole integral to different part. Step 2: you add the powers back and divide the power. Step 3:Now you simplify the whole thing and you will get the answer.

Find the answer to the following: ***Be careful when you take the anti-derivative of the trigonometry ***

Find the answer to the following: Step 1:to do this question you have to do the substitution first. Step 2:Now take the derivative of u. Step 3: substitute du into the equation. Step 4: Solve. Step 5: substitute u back to the answer.