Math 180 4.8 – Antiderivatives 1. Sometimes we know the derivative of a function, and want to find the original function. (ex: finding displacement from.

Slides:

Advertisements

Similar presentations

6.2 Antidifferentiation by Substitution

Advertisements

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

E1 - Antiderivatives and Indefinite Integrals

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.

Warm-up: 1)If a particle has a velocity function defined by, find its acceleration function. 2)If a particle has an acceleration function defined by, what.

Antidifferentiation TS: Making decisions after reflection and review.

Section 4.3 Indefinite Integrals and Net Change Theorem Math 1231: Single-Variable Calculus.

5.c – The Fundamental Theorem of Calculus and Definite Integrals.

6.2 Integration by Substitution & Separable Differential Equations.

Section 4.1 – Antiderivatives and Indefinite Integration.

Section 6.2: Integration by Substitution

4.1 The Indefinite Integral. Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is.

Remember that given a position function we can find the velocity by evaluating the derivative of the position function with respect to time at the particular.

MAT 1221 survey of Calculus Section 6.1 Antiderivatives and Indefinite Integrals

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.

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:

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.

4.1 ANTIDERIVATIVES & INDEFINITE INTEGRATION. Definition of Antiderivative  A function is an antiderivative of f on an interval I if F’(x) = f(x) for.

4001 ANTIDERIVATIVES AND INDEFINITE INTEGRATION

13.1 Antiderivatives and Indefinite Integrals. The Antiderivative The reverse operation of finding a derivative is called the antiderivative. A function.

1 Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is Lecture 17 The Indefinite Integral Waner.

Antiderivatives and Indefinite Integration. 1. Verify the statement by showing that the derivative of the right side equals the integrand of the left.

4.1 Antiderivatives and Indefinite Integration Definition of Antiderivative: A function F is called an antiderivative of the function f if for every x.

Antiderivatives. Mr. Baird knows the velocity of particle and wants to know its position at a given time Ms. Bertsos knows the rate a population of bacteria.

Calculus - Santowski 12/8/2015 Calculus - Santowski 1 C Indefinite Integrals.

7.1: Antiderivatives Objectives: To find the antiderivative of a function using the rules of antidifferentiation To find the indefinite integral To apply.

Warm-Up 4-1: Antiderivatives & Indefinite Integrals ©2002 Roy L. Gover ( Objectives: Define the antiderivative (indefinite integral)

In this section, we introduce the idea of the indefinite integral. We also look at the process of variable substitution to find antiderivatives of more.

Write the derivative for each of the following.. Calculus Indefinite Integrals Tuesday, December 15, 2015 (with a hint of the definite integral)

ANTIDERIVATIVES AND INDEFINITE INTEGRATION AB Calculus.

ANTIDERIVATIVES Definition: reverse operation of finding a derivative.

5.a – Antiderivatives and The Indefinite Integral.

Distance Traveled Area Under a curve Antiderivatives

Integration Techniques, L’Hôpital’s Rule, and Improper Integrals Copyright © Cengage Learning. All rights reserved.

Differential Equations Linear Equations with Variable Coefficients.

Warm Up. Solving Differential Equations General and Particular solutions.

 y’ = 3x and y’ = x are examples of differential equations  Differential Form dy = f(x) dx.

January 25th, 2013 Antiderivatives & Indefinite Integration (4.1)

Aim: How to Find the Antiderivative Course: Calculus Do Now: Aim: What is the flip side of the derivative? If f(x) = 3x 2 is the derivative a function,

Barnett/Ziegler/Byleen Business Calculus 11e1 Learning Objectives for Section 13.2 Integration by Substitution ■ The student will be able to integrate.

SECTION 4-1 Antidifferentiation Indefinite Integration.

Chapter 4 Integration 4.1 Antidifferentiation and Indefinate Integrals.

Antiderivatives and Indefinite Integrals Modified by Mrs. King from Paul's Online Math Tutorials and Notes

Calculus 6.1 Antiderivatives and Indefinite Integration.

Introduction to Integrals Unit 4 Day 1. Do Now  Write a function for which dy / dx = 2 x.  Can you think of more than one?

Inverse Trigonometric Functions: Differentiation & Integration (5. 6/5

Indefinite Integrals or Antiderivatives

6.1 – 6.3 Differential Equations

Antiderivatives 5.1.

Antidifferentiation and Indefinite Integrals

Lesson 4.5 Integration by Substitution

MTH1170 The Fundamental Theorem of Calculus

Copyright (c) 2003 Brooks/Cole, a division of Thomson Learning, Inc.

Section 4.1 – Antiderivatives and Indefinite Integration

Fundamental Concepts of Integral Calculus

and Indefinite Integration (Part I)

4.1 Antiderivatives and Indefinite Integration

The Fundamental Theorem of Calculus (FTC)

Section Indefinite Integrals

Chapter 4 Integration.

6.1: Antiderivatives and Indefinite Integrals

Integration by Substitution (Section 4-5)

4.5 Integration by Substitution The chain rule allows us to differentiate a wide variety of functions, but we are able to find antiderivatives for.

Integral Defined Functions Day 1

Section Indefinite Integrals

The Indefinite Integral

Sec 5.4: INDEFINITE INTEGRALS AND THE NET CHANGE THEOREM

1. Antiderivatives and Indefinite Integration

Section 2 Integration by Substitution

Presentation transcript:

Math – Antiderivatives 1

Sometimes we know the derivative of a function, and want to find the original function. (ex: finding displacement from velocity.) 2

3

4 antiderivative

5

6

7

8

9

Let’s fill out the following table of antiderivatives: 10 FunctionGeneral antiderivative

11

12

13 indefinite integral

14 indefinite integral integral sign

15 indefinite integral integral sign integrand

16 indefinite integral integral sign integrand variable of integration

17

18

19

20

21

22 differential equation

23 differential equation

24 differential equation

25 differential equation general solution

26

27 initial condition

28 initial condition

29 initial condition particular solution

30

31 initial value problem

32 initial value problem