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

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More Trig Integrals
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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

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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

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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'
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Assignment

• Lesson 9.3
• Page 369
• Exercises 1 37 every other odd, 43, 45,
  49