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)

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Presentation transcript:

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

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

Trig Integrals (9/17/12) Trig integrals can often be done by recalling the basic trig derivatives and using some basic trig identities: sin 2 (x) + cos 2 (x) = tan 2 (x) = sec 2 (x) (“Pythagorean Identities”) cos(2x) = cos 2 (x) – sin 2 (x) (“Double angles”) = 2cos 2 (x) – 1 = 1 – 2sin 2 (x)

Three Examples  sin 2 (x) cos 3 (x) dx ??  tan(x) sec 4 (x) dx ??  sin 2 (x) dx

Clicker Question 3 What is  sin 3 (x) dx ? – A. cos(x) – (1/3)cos 3 (x) + C – B. (1/3)cos 3 (x) – cos(x) + C – C. x – (1/3)cos 3 (x) + C – D. (1/3)cos 3 (x) – x + C – E. (1/4)sin 4 (x) + C

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)

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