Trig and Hyperbolic Integrals Lesson 9.3

Basic Trig Integrals

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

Integration of tan x Recall that Thus Which gives us

More Trig Integrals

Try This! Manipulation of the integrand expression is a useful strategy

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

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

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

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'

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