September 10, 2009
No CommentsHow to Solve an Integration Problem by Trigonometric Substitution
Description
This video clearly illustrates how to solve an integration problem using trigonometric substitution. One example problem is provided in the video.
Overview
Trigonometric substitution works the same way as normal substitution, only you substitute in trigonometric functions, and each trigonometric function can only be substituted for a particular pattern. These are the patterns to watch for and what you can substitute in for them:
a^2 – x^2 uses x = a * sin(theta)
a^2 + x^2 uses x = a * tan(theta)
x^2 – a^2 uses x = a * sec(theta)
All of these also have the option of including a square root with them, but it doesn’t matter – you can use the substitution without the square root. Normally after finding the x value you will take a derivative so you have the value of dx To find other values needed,SOHCAHTOA is often used with a right triangle picture. Once all of your values have been solved for, you can plug them all back into your original equation and solve.
