8. Integration by Trigonometric Substitution

by M. Bourne

In this section, we see how to integrate expressions like

math expression

We substitute the following to simplify the expressions to be integrated:

math expression

Example 1: math expression


Answer

How are you going??

math expression Don't give up!!

Example 2: math expression.


First, the LiveMath solution to this problem:

LIVEMath


Answer

Exercises

Integrate each of the given functions:

1. math expression


Answer

2. math expression


Answer

3. math expression


Answer


Win a scholarship through Zinch. Double your money!

Find your integral using Mathematica!

Enter multiply using *, square root of x using Sqrt[x] and trigonometry like Sin[x]. See the full list of how to enter math.

Click the blue button to find your integral.


Didn't find what you are looking for on this page? Try search:

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.

Calculus Lessons on DVD

get MathTutorDVDs

Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

 

Book mark this page

Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...

 


Need a break? Play a math game. Well, they all involve math... No, really!

dumbolf memoTST bola shadow factory mindfields trick-hoops-challenge crystal clear