# Integration with Trigonometric Substitution

#### janofano

[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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#### 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
$$u=x^2\sqrt{9-x^2}dx$$

Last edited:

"Integration with Trigonometric Substitution"

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