Integration with Trigonometric Substitution

[janofano]

[SOLVED] Integration with Trigonometric Substitution

Homework Statement

Given integral (I):
I[(x)sqrt(9-x^2)dx]

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

Use proper trigonometric substitution to solve this problem.

Homework Equations

The Attempt at a Solution

 

[rocomath]

You don't even need Trig substitution.

\int x\sqrt{9-x^2}dx

u=9-x^2
du=-2xdx \rightarrow xdx=-\frac 1 2 du

 

[janofano]

I know that I don't need that.
But the problem is, I have to use it.
The exercise require it.

 

[rocomath]

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.

 

[Vid]

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

 

[janofano]

\int x^2\sqrt{9-x^2}dx
apropo
u=x^2\sqrt{9-x^2}dx