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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:
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
Ex(1) Use the Definite Integral rules and the given information to find each integral.
Exercises: Page 294 # 1 5 odd
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
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
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
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) = ____
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
FUNCTIONf(x)
ANTIDERIVATIVEF(x)
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
FUNCTIONf(x)
ANTIDERIVATIVEF(x)
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
Ex(2) Find the function, f(x) that satisfies the given conditions:
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
Exercises: Page 207 # 29 37 odd
Worksheet 6.3 # 19 odd, 13, 1925 odd, 29, 33, 35
Answer should be
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
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.
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Notes Day 2 6.3 Definite Integrals and Antiderivatives.notebook May 30, 2018
Ex(3) Find each of the following indefinite integrals.
Exercises: Indefinite Integrals Worksheet