## [SOLVED] Integration with Trigonometric Substitution

1. The problem statement, all variables and given/known data

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.
2. Relevant equations

3. The attempt at a solution
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 You don't even need Trig substitution. $$\int x\sqrt{9-x^2}dx$$ $$u=9-x^2$$ $$du=-2xdx \rightarrow xdx=-\frac 1 2 du$$
 I know that I don't need that. But the problem is, I have to use it. The exercise require it.

## [SOLVED] 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.
 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
 $$\int x^2\sqrt{9-x^2}dx$$ apropo $$u=x^2\sqrt{9-x^2}dx$$

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