- #1

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**[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.

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- Thread starter janofano
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- #1

- 4

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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

- 1,753

- 1

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

[tex]u=9-x^2[/tex]

[tex]du=-2xdx \rightarrow xdx=-\frac 1 2 du[/tex]

- #3

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I know that I don't need that.

But the problem is, I have to use it.

The exercise require it.

But the problem is, I have to use it.

The exercise require it.

- #4

- 1,753

- 1

- #5

- 401

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x = 3sin(u)

dx = 3cos(u)du

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

So the integral becomes 27sin(u)cos^2(u)du

- #6

- 4

- 0

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

apropo

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

apropo

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

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