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 = π/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, , 45, 49