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## Main Question or Discussion Point

How do I integrate sqrt(x/2-x)dx?

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How do I integrate sqrt(x/2-x)dx?

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[itex]\int\sqrt{\frac{x}{2}-x}\space dx[/itex] or [itex]\int\sqrt \frac{x}{2-x}\space dx[/itex] ?

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Infrared

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Use the substitution [itex] u= \sqrt{2-x} [/itex] to turn the integral into [itex] -2 \int \sqrt{2-u^2} du [/itex], which you can do by trig substitution.

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Yes,it this one.I know U substitution, but I think I miss out something.How did you change [itex] u= \sqrt{2-x} [/itex] to turn the integral into [itex] -2 \int \sqrt{2-u^2} du [/itex]

Use the substitution [itex] u= \sqrt{2-x} [/itex] to turn the integral into [itex] -2 \int \sqrt{2-u^2} du [/itex], which you can do by trig substitution.

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Infrared

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When you said trigonometric substitution, you mean a^2-x^2=1-sin^2(x)?

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Infrared

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