Definite%20Integrals

1
Definite Integrals

• Day 5

2
So what have we learned?

• We have learned that if you integrate a function,
  you find an expression to determine the area
  under that curve.

f(x)
3
What if we have two curves?

• What would the area between these two curves be?

4
How about these two curves?
From a to b, what is true about
Is the equation going to change?
5
Lets look at some animations

• This is a Riemann Sum Area between curves

6

• Many problems here will ask you to find the area
  between two curves without defining a and b.
  This means you have to find a and b.
• If both equations are y in terms of x, set them
  equal and solve for x. Then do a quick sketch.
  THEN and only then pull out your calculator to
  make sure you are correct, and continue.

7
Why cant I always use my calculator?

• Because on tests and on a good portion of the AP
  exam you wont be able to use your calculator
  anyway. Tomorrow well learn how to integrate on
  the calculator. BUT as this tool wont be
  available to you on tests, you need to understand
  and be able to do this work. The calculator
  simply checks your work for you.

8
Examples

• Find the area between the curves