Trig and Hyperbolic Integrals - PowerPoint PPT Presentation

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Trig and Hyperbolic Integrals

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8. Integrals of Hyperbolic Functions. Recall derivatives of ... Application. Electric wires suspended between two towers form a catenary with the equation ... – PowerPoint PPT presentation

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Title: Trig and Hyperbolic Integrals


1
Trig and Hyperbolic Integrals
  • Lesson 9.3

2
Basic Trig Integrals
3
Using the Trig Integrals
  • The technique is often to find a u which is the
    angle, the argument of the trig function
  • Consider
  • What is the u, the du?
  • Substitute, integrate

4
Integration of tan x
  • Recall that
  • Thus
  • Which gives us

5
More Trig Integrals
6
Try This!
  • Manipulation of the integrand expression is a
    useful strategy

7
Application
  • Find the area bounded by y sec x, y x, x
    0, and x p/4
  • What is the height and width of each slice?
  • Height sec xi xi
  • Width ?x
  • Integral

8
Integrals of Hyperbolic Functions
  • Recall derivatives of hyperbolic functions
  • Section 8.6, Page 341
  • We now use these to specify integrals

9
Example
  • Try
  • What should be the u, the du?
  • Substitute, integrate

10
Application
  • Electric wires suspended between two towers form
    a catenary with the equation
  • If the towers are 120 ft apart, what is the
    length of the suspended wire?
  • Use the arc length formula

120'
11
Assignment
  • Lesson 9.3
  • Page 369
  • Exercises 1 37 every other odd, 43, 45,
    49
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