Register to reply

Integration with Trigonometric Substitution

Share this thread:
Mar2-08, 12:21 PM
P: 4
1. The problem statement, all variables and given/known data

Given integral (I):

by words:
Integral of "X" times square root of "9-X(squared)

Use proper trigonometric substitution to solve this problem.
2. Relevant equations

3. The attempt at a solution
Attached Thumbnails
Attached Images
Phys.Org News Partner Science news on
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
Mar2-08, 12:29 PM
rocomath's Avatar
P: 1,756
You don't even need Trig substitution.

[tex]\int x\sqrt{9-x^2}dx[/tex]

[tex]du=-2xdx \rightarrow xdx=-\frac 1 2 du[/tex]
Mar2-08, 12:31 PM
P: 4
I know that I don't need that.
But the problem is, I have to use it.
The exercise require it.

Mar2-08, 01:21 PM
rocomath's Avatar
P: 1,756
Integration with Trigonometric Substitution

Well you posted the solution to it? I don't know what else to tell you. Just analyze what they did. Work it yourself a couple times if you have to.
Mar2-08, 01:57 PM
P: 420
You forgot a term when you first did the substitution.

x = 3sin(u)
dx = 3cos(u)du

(9 - x^2)^(1/2) = 3cos(u)

So the integral becomes 27sin(u)cos^2(u)du
Mar3-08, 02:58 PM
P: 4
[tex]\int x^2\sqrt{9-x^2}dx[/tex]

Register to reply

Related Discussions
Trigonometric Substitution Calculus & Beyond Homework 4
Integration using substitution Calculus & Beyond Homework 3
Integration by Trigonometric Substitution. Calculus & Beyond Homework 9
Integration By Parts and Substitution Calculus & Beyond Homework 13
Integration, u substitution, 1/u Calculus & Beyond Homework 16