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## Homework Statement

[itex]\int_{1}^{5}\sqrt{4-(x-3)^2}dx[/itex]

## Homework Equations

## The Attempt at a Solution

Not really a homework. Just curious.

Let [itex]x-3=2sin u[/itex]

[itex]x=2sin u+3[/itex]

Now limit change,

when x=1, u = arcsin (-1)

when x=5, u = arcsin (1)

Since there are infinitely many solution of arcsin (-1) and arcsin (1), How do we know which ones to choose?

Thank you very much

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