Supplemental Notes

1
Supplemental Notes

• Chapter 5
• Section 4

2
Correct PS 5-2 (182)
3
Section 5-4 Objective

• Become familiar with the symbol used for an
  indefinite integral or an antiderivative by using
  this symbol to evaluate indefinite integrals.
• Indefinite integral is another name for
  antiderivative.

4
Before and After the lazy mathematician strikes
again
The integral sign is a stretched out S this
is related to what we did with the trapezoid
rule. We make a bunch of trapezoids, find their
areas, then add them all up, or take the Sum.
5
Definition Indefinite Integral

• The integral of f(x) with respect to x
• Note that the indefinite integral is itself a
  function. The symbol represents something being
  done to the function f(x).

6
Properties that make the process easier (like
that is possible)

• Integral of a constant times a function
• Integral of a sum of two functions

7
And now for the magic trick
But, we dont like u!

• That looks complicated, but if we say
• Then rewrite in terms of u, we get
• So everywhere u is,

8
Homework, at last!

• Problem set 5-4
• Pages 193-195
• 2-eternity (even), and number 43.