Presentation is loading. Please wait.

Presentation is loading. Please wait.

Indefinite Integrals 6.1. Integration - Antidifferentiation - method of solution to a differential equation INdefinite Integral Integration Symbol Variable.

Published byJosef Kenning Modified over 9 years ago

Similar presentations

Presentation on theme: "Indefinite Integrals 6.1. Integration - Antidifferentiation - method of solution to a differential equation INdefinite Integral Integration Symbol Variable."— Presentation transcript:

1 Indefinite Integrals 6.1

2 Integration - Antidifferentiation - method of solution to a differential equation INdefinite Integral Integration Symbol Variable of Integration Integrand Constant of Integration

3

4 Solve the differential equation SEPARATE VARIABLES (1) INTEGRATE BOTH SIDES Constant of Integration

5 Find the general solution to SEPARATE VARIABLES (2) INTEGRATE BOTH SIDES Constant of Integration

6 Find the general solution to SEPARATE VARIABLES (3) INTEGRATE BOTH SIDES Constant of Integration Note: This IS a solved differential equation General Solution since we don’t know C

7 Solve the differential equation SEPARATE VARIABLES (1) INTEGRATE BOTH SIDES Constant of Integration

8 Find the general solution to SEPARATE VARIABLES (2) INTEGRATE BOTH SIDES Constant of Integration

9 POSITION s(t) VELOCITY v(t) ACCELERATION a(t) DIFFERENTIATEDIFFERENTIATE INTEGRATEINTEGRATE

Download ppt "Indefinite Integrals 6.1. Integration - Antidifferentiation - method of solution to a differential equation INdefinite Integral Integration Symbol Variable."

Similar presentations

Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.
4.1 Antiderivatives and Indefinite Integrals Defn. A function F(x) is an antiderivative of f(x) on an interval I if F '(x)=f(x) for all x in I. ex. Find.

4.1 Antiderivatives and Indefinite Integrals Defn. A function F(x) is an antiderivative of f(x) on an interval I if F '(x)=f(x) for all x in I. ex. Find.
Solving Absolute Value Equations

Solving Absolute Value Equations
Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.

Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.
1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.
A) Find the velocity of the particle at t=8 seconds. a) Find the position of the particle at t=4 seconds. WARMUP.

A) Find the velocity of the particle at t=8 seconds. a) Find the position of the particle at t=4 seconds. WARMUP.
1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.
Method Homogeneous Equations Reducible to separable.

Method Homogeneous Equations Reducible to separable.
Exponential Growth and Decay

Exponential Growth and Decay
3.5 – Solving Systems of Equations in Three Variables.

3.5 – Solving Systems of Equations in Three Variables.
2-4 Solving Equations with Variables on Both Sides.

2-4 Solving Equations with Variables on Both Sides.
Section 6.1 Polynomial Derivatives, Product Rule, Quotient Rule.

Section 6.1 Polynomial Derivatives, Product Rule, Quotient Rule.
Mathematics. Session Differential Equations - 2 Session Objectives  Method of Solution: Separation of Variables  Differential Equation of first Order.

Mathematics. Session Differential Equations - 2 Session Objectives  Method of Solution: Separation of Variables  Differential Equation of first Order.
4.1 The Indefinite Integral. Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is.

4.1 The Indefinite Integral. Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is.
Solving Equations with the Variable on Each Side 2.4.

Solving Equations with the Variable on Each Side 2.4.
Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.
Sec. 4.1 Antiderivatives and Indefinite Integration By Dr. Julia Arnold.

Sec. 4.1 Antiderivatives and Indefinite Integration By Dr. Julia Arnold.
Math 140 5.1 – Antidifferentiation: The Indefinite Integral 1.

Math – Antidifferentiation: The Indefinite Integral 1.
4.1 Antiderivatives and Indefinite Integration. Suppose you were asked to find a function F whose derivative is From your knowledge of derivatives, you.

4.1 Antiderivatives and Indefinite Integration. Suppose you were asked to find a function F whose derivative is From your knowledge of derivatives, you.
Antiderivatives Indefinite Integrals. Definition  A function F is an antiderivative of f on an interval I if F’(x) = f(x) for all x in I.  Example:

Antiderivatives Indefinite Integrals. Definition  A function F is an antiderivative of f on an interval I if F’(x) = f(x) for all x in I.  Example:

Similar presentations

Ads by Google