6.3 Definite Integrals & Antiderivatives Zero Rule · Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018 The family of all the antiderivatives of a function

Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018

6.3 Definite Integrals & Antiderivatives

Rules for Definite Integrals

Zero Rule:

Order of Integration Rule:

Additivity Rule:

Constant Multiple Rule:

Sum and Difference Rule:


Ex(1) Use the Definite Integral rules and the given information to find each integral.

Exercises: Page 294 # 1 5 odd


A function F(x) is called an antiderivative of f(x) on an interval if F '(x) = f(x) for all x in the interval

FUNCTIONf(x)

ANTIDERIVATIVEF(x)

Antiderivative Rules

Ex(1) Find all possible functions with the given derivative

...... answer would be written as f(x) = ___

Question could be asked as:

Ex(1) Find the antiderivative of the function

..... answer would be written as F(x) = ___

OR


Ex(1) Find all possible functions with the given derivative

FUNCTIONf(x)

ANTIDERIVATIVEF(x)

FUNCTIONf(x)

ANTIDERIVATIVEF(x)

Find the antiderivative (but given f(x) = 3x + 5 )Answer written as F(x) = ____


FUNCTIONf(x)

ANTIDERIVATIVEF(x)


FUNCTIONf(x)

ANTIDERIVATIVEF(x)


Ex(2) Find the function, f(x) that satisfies the given conditions:


Exercises: Page 207 # 29 37 odd

Worksheet 6.3 # 19 odd, 13, 1925 odd, 29, 33, 35

Answer should be


The family of all the antiderivatives of a function f(x) is the indefinite integral of f with respect to x and is denoted by

Indefinite Integral Rules

These should look very similar

to the antiderivative

rules.

There are also some new ones

listed here.


Ex(3) Find each of the following indefinite integrals.

Exercises: Indefinite Integrals Worksheet

6.3 Definite Integrals & Antiderivatives Zero Rule · Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018 The family of all the antiderivatives of a function

Documents