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.

Slides:

Advertisements

Similar presentations

Warm Up 1) Is (-3, 4) a solution to the system? 2)Solve the system by graphing y = -2x + 5 2y = x - 2.

Advertisements

Solving Quadratic/Linear Systems Algebraically Integrated A2/trig.

Lesson 9.7 Solve Systems with Quadratic Equations

3.5 – Solving Systems of Equations in Three Variables.

AP Calculus Jeopardy Final Jeopardy Limits Derivatives or Limits Derivatives Integrals Integrals Misc. Potpour ri Q $100 Q $200 Q $300 Q $400 Q $500.

Differential Equations. Definition A differential equation is an equation involving derivatives of an unknown function and possibly the function itself.

Areas & Definite Integrals TS: Explicitly assessing information and drawing conclusions.

Substitution Method Critical Thinking Skill: Explicitly assess information and draw conclusions Sometimes using the graphing method can be problematic.

Differential Equations: Growth and Decay Calculus 5.6.

1.3 Solving Systems by Substitution. Steps for Substitution 1.Solve for the “easiest” variable 2.Substitute this expression into the other equation 3.Solve.

MAT 213 Brief Calculus Section 5.6 Integration by Substitution or Algebraic Manipulation.

5.3 – Solving Multi-Step Inequalities. *Just like solving equations*

Sect. 4.1 Antiderivatives Sect. 4.2 Area Sect. 4.3 Riemann Sums/Definite Integrals Sect. 4.4 FTC and Average Value Sect. 4.5 Integration by Substitution.

Exponential Growth and Decay 6.4. Separation of Variables When we have a first order differential equation which is implicitly defined, we can try to.

MAT 1235 Calculus II Section 6.5 Exponential Growth and Decay

MAT 3237 Differential Equations Section 2.2 Separable Equations

MAT 125 – Applied Calculus Exponential Functions as Mathematical Models.

AIM: How do we solve systems using substitution? Topic: Solving systems algebraically.

Solving Linear Systems by Substitution

Substituting into expressions.

Warm Up. Solving Differential Equations General and Particular solutions.

Warm up Problems More With Integrals It can be helpful to guess and adjust Ex.

Section 6.2 Differential Equations: Growth and Decay.

Particular Solutions to Differential Equations Unit 4 Day 2.

Solving a System of Equations in Two Variables By Substitution Chapter 8.2.

Chapter 6 Integration Section 3 Differential Equations; Growth and Decay.

The Substitution Method Objectives: To solve a system of equations by substituting for a variable.

Warm-up. Systems of Equations: Substitution Solving by Substitution 1)Solve one of the equations for a variable. 2)Substitute the expression from step.

Notes 6.5, Date__________ (Substitution). To solve using Substitution: 1.Solve one equation for one variable (choose the variable with a coefficient of.

Problem of the Day - Calculator Let f be the function given by f(x) = 2e4x. For what value of x is the slope of the line tangent to the graph of f at (x,

An Introduction to MathCAD More Symbolic Maths And First Steps in Calculus.

2.4 – Solving Equations with the Variable on Each Side.

Algebra Review. Systems of Equations Review: Substitution Linear Combination 2 Methods to Solve:

OBJ: Solve Linear systems graphically & algebraically Do Now: Solve GRAPHICALLY 1) y = 2x – 4 y = x - 1 Do Now: Solve ALGEBRAICALLY *Substitution OR Linear.

Solving Systems by Substitution (isolated) Solving Systems by Substitution (not isolated)

Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions.

Today in Algebra 2 Get a calculator. Go over homework Notes: –Solving Systems of Equations using Elimination Homework.

Equations Quadratic in form factorable equations

Chapter 12 Section 1.

1-5 Equations Goals: Solve equations with one variable

Systems of Equations Lesson 41: Solve by using a matrix

Honors Algebra II 3.5 Solving Systems with Three Variables.

3-2: Solving Systems of Equations using Substitution

Warm-Up Solve the system by substitution..

6-2 Solving Systems Using Substitution

Solving Linear Systems Algebraically

Solve a system of linear equation in two variables

3-2: Solving Systems of Equations using Substitution

Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3.2a – Solving Systems algebraically

Evaluate the expression if w = -4, x = 2, y = ½, and z = |6 + z| - |7| Original problem. |6 + (-6)| - |7| Substitute values for the variables.

Notes Solving a System by Elimination

Notes Solving a System by Elimination

Write Equations of Lines

Solving Systems of Linear and Quadratic Equations

Warm-Up Solve the system by graphing..

3-2: Solving Systems of Equations using Substitution

Equations Quadratic in form factorable equations

Section 8.5 Day 1 Using the Distributive Property

1-2 Solving Linear Systems

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

3-2: Solving Systems of Equations using Substitution

Solving Equations in Quadratic Form

Warm- Up: Solve by Substitution

Evaluating an expression with one variable

Presentation transcript:

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 Express the final answer in term of x

Yah! We are done. What have you studied in MAT 116? What is Calculus?

What is “calculus”? –Calculus is the study of how things change. What do you learn in a calculus class? –Functions, limits, derivatives, integrals, … Derivatives can used to study applications that involve the rate of change such as population growth, radioactive decay, optimization problems, … Integrals can be used to calculate the area, equation of a curve, business sales, … How do algebra and calculus differ? Ex: Solving equations to find a particular value of a variable Ex: How a change in a variable affects another variable?