Properties of integrals.

1. http://tinyurl.com/78l246

2. The Fundamental Theorem of Calculus ... part I
Let the function ƒ be continuous on [a, b] with derivative ƒ'. Then ...
Total change in ƒ
In words: Integrating a rate of change function ƒ' over an interval [a, b]
gives the total change in ƒ, ƒ(b) - ƒ(a), over the same interval.
In other words, the integral of a derivative is the same thing as
the total change in it's parent function over the same interval.
Also recall:
and ...

3. Use The Fundamental Theorem of Calculus to evaluate:

4. Properties of Integrals ...
Additive Interval Rule
Constant Multiple Rule
Sum and Difference Rule Inequality Rule
If ƒ(x) ≤ g(x) for all x
Let's see some examples ...

5. Constant Multiple Rule Consider each of these integrals and the
related graphs

6. Combining this rule with the
Sum and Difference Rule
constant multiple rules allows us
to integrate expressions like this:

7. Additive Interval Rule This rule is illustrated in the graph below.
It allows us to solve problems like this
one:
Given: and
Find:
Ye Olde Buh-ket Build your own equations from the bucket:
-3 O Integrals +
= –
–
= -3 4
= – =
4

9. Consider each of these integrals and the
Inequality Rule
related graphs
If ƒ(x) ≤ g(x) for all x