1 / 7

Understanding Trigonometric Integrals and Antiderivatives

This content focuses on the techniques involved in evaluating trigonometric integrals and antiderivatives. It includes example problems, such as the integration of functions like ( int x sin(3x) , dx ) and other common trigonometric forms. Key identities such as Pythagorean and double angle formulas are discussed, along with a non-obvious antiderivative of tan and sec functions. Students are encouraged to practice problems from their textbook to reinforce their understanding of these concepts.

nehru-manning
Download Presentation

Understanding Trigonometric Integrals and Antiderivatives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related