6.1 Antiderivatives and Indefinite Integration
Objectives: 1.) Understand the concept of a antiderivative 2.) Use differentiation rules to produce and use
antidifferentiation rules.
Vocab
ā¢ Differential: the differential is an equation that relates the change in y with respect to the change in x.
dy = fā(x)dx
Vocabulary
f(x)= x3 + 2x
fā(x)= 3x2 + 2
What was the function that WAS derived to get this?
We are going to start going backwards now. We are going to UNDERIVE functionsā¦
The antiderivative function, notated BIG F, is the fuction that was derived to get a function f.
Fā(x) = f(x) for all x in I
f(x)
F(x)
Integration and antidifferentiation mean the same thing
ā¢ The process of underiving
Notation
CxFxdxfy )()(
Notation/Representation
ā¢ We call G(x) the general antiderivative of f.G(x) = F(x) + C for all x in I the indefinite integral .
ā¢ C is called the constant of integration. It is the constant number that could have been wiped out in differentiation. When we antidifferentiate, we need to consider a constant may have been there.
ā¢ Consider f(x) = x2 + 1
ā¢ General antiderivative and General Solution are synonomous.
Anyone of these graphs could have produced fā(x) = 2x
Basic Rules of Integration (pg. 390)Integration of ZERO
Integration of a constant
Integration of a power
Integration with a scalar multiple
Integration of sums and differences
Homework:
ā¢ Pg 394 #1; 4; 9-13(odd); 19-23(odd); 26; 28-31; 37-39;
42; 43
Examples
Objectives
1.) Apply integration to vertical motion functionsā¦
2.) Start thinking forwardsā¦ backwards.
Particular Solution vs. General Solution
ā¢ http://www.mathworksheetsgo.com/tools/free-online-graphing-calculator.php