Clicker Question 1 What is x sin(3x) dx ? A. (1/3)cos(3x) + C

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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(e2 – 1) C. ¼(e2 + 1) D. 4(e2 + 1) E. e + 1

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 = 1 – 2sin2(x)

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

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.