1. Clicker Question 1 What is x sin(3x) dx ? A. (1/3)cos(3x) + C
B. (-1/3)x cos(3x) + (1/9)sin(3x) + C
C. -x cos(3x) + sin(3x) + C
D. -3x cos(3x) + 9sin(3x) + C
E. (1/3)x cos(3x) - (1/9)sin(3x) + C

2. Clicker Question 2 What is ? A. e – 1 B. ¼(e2 – 1) C. ¼(e2 + 1)
D. 4(e2 + 1)
E. e + 1

3. Trig Integrals (9/16/13)
Trig integrals can often be done by recalling the basic trig derivatives and using some basic trig identities:
sin2(x) + cos2(x) = 1
1 + tan2(x) = sec2(x) (“Pythagorean Identities”)
cos(2x) = cos2(x) – sin2(x) (“Double angles”) = 2cos2(x) – = 1 – 2sin2(x)

4. Three Examples sin2(x) cos3(x) dx ?? tan(x) sec4(x) dx ??
 sin2(x) dx

5. Two Basic But Non-Obvious Trig Antiderivative Facts
tan(x) dx ?? Hint: Use sin, cos and substitution.
sec(x) dx ?? Hint: Multiply top and bottom by sec(x) + tan(x)

6. Assignment for Wednesday
Read Section 7.2.
Do Exercises 3, 7, 13, 23, and 61.