Integration Using Trigonometric Substitution Brought to you by Tutorial Services – The Math Center

Objective To eliminate radicals in the integrand using Trigonometric Substitution For integrals involving use u = a sin For integrals involving use u = a tan For integrals involving use u = a sec

For integrals involving Let u = a sin Inside the radical you will have Using the Pythagorean Identities, that is equal to This will result in = a cos

For integrals involving Let u = a tan Inside the radical you will have Using the Pythagorean Identities, that is equal to This will result in = a sec

For integrals involving Let u = a sec Inside the radical you will have Using the Pythagorean Identities, that is equal to This will result in = + a tan Positive if u > a, Negative if u < - a

Converting Limits By converting limits, you avoid changing back to x, after you are done with the integration Because has the form then u = x, a = 3, and x = 3 sin

Converting Limits Now, when x = 0, the Lower Limits is: 0 = 3 sin Now, when x = 3, the Upper Limit is: 3 = 3 sin 1 = sin /2 =

Examples Solve the following integrals:

Integration Using Trigonometric Substitution Links Integration Using Trigonometric Substitution Handout Trigonometric Identities Handout Integrals and Derivatives Handout Trigonometric Substitution Quiz