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Clicker Question 1

Clicker Question 1. What is  x sin(3 x ) d x ? A. (1/3)cos(3 x ) + C B. (-1/3) x cos(3 x ) + (1/9)sin(3 x ) + C C. - x cos(3 x ) + sin(3 x ) + C D. -3 x cos(3 x ) + 9sin(3 x ) + C E. (1/3) x cos(3 x ) - (1/9)sin(3 x ) + C. Clicker Question 2. What is ?

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Clicker Question 1

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  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 (2/7/14) • 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)

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

  5. Clicker Question 3 • What is sin3(x) dx ? • A.cos(x) – (1/3)cos3(x) + C • B.(1/3)cos3(x) – cos(x) + C • C. x – (1/3)cos3(x) + C • D. (1/3)cos3(x) – x + C • E. (1/4)sin4(x) + C

  6. Another Non-Obvious Trig Antiderivative Fact • Recall that tan(x) dx = -ln(cos(x)) + C = ln(sec(x)) + C • What is sec(x) dx ?? (Hint: Multiply top and bottom by sec(x) + tan(x))

  7. Assignment for Monday • Read Section 7.2. • Do Exercises 3, 7, 13 (Hint: We worked out in class what an antiderivative of sin2(t) is), 23, 55, 61.

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