1. 7-2 Antidifferentiation by substitution

2. An indefinite integral with respect to x is
*Notes: A definite integral is a number
An indefinite integral is a family of functions
Ex 1) Evaluate

3. Review of Some Important Antiderivatives
Properties
Power Formulas

4. Review of Some Important Antiderivatives
Trigonometry
Exponents & Logarithmic

5. Note: WE have to be REALLY CAREFUL of what the question is asking
*Note: WE have to be REALLY CAREFUL of what the question is asking! WATCH THE NOTATION!
Ex 3) Let f (x) = x3 + 1 and let u = x2. Find each of the following antiderivatives in terms of x.

6. Substitution
A complete substitution will take and change it to
The goal is to look for something that is the derivative of something else in the problem
This takes practice! Be patient with yourself as you learn how to do these.
Ex 4) Evaluate
Let u = cos x
du = –sin x dx
–1du = sin x dx

7. Ex 5) Evaluate
Ex 6) Evaluate

8. Evaluating Definite Integrals
*Note: If you adjust limits – you don’t have to substitute back
Ex 8)

9. Ex 9) Evaluate

10. homework
Pg. 342 #1 – 43 (mult of 1+3n), 53 – 61 odd