MATH 2B Chapter Notes - Chapter 7.2: Fo Tan, Trigonometric Integral, Scilab

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

The three identities sin2 x + cos2 x = 1, cos2 x = 1. 2 (1 cos 2x) can be used to integrate expressions involving powers of sine and cosine. The basic idea is to use an identity to put your integral in a form where one of the substituions u = sin x or u = cos x may be applied. 2 (cos 2x + 1) and sin2 x = 1. Examples: to compute z sin3 x dx, we rst apply the identity sin2 x + cos2 x = 1 to get. Z sin3 x dx = z sin x(1 cos2 x) dx. This is now set up perfectly for the substitution u = cos x = du = sin x dx: Z sin3 x dx = z (1 u2)( du) = z u2 1 du cos3 x cos x + c u3 u + c = 3: the same trick works in the following: