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Question
Integrate the following with respect to x.
`sqrt(1 - sin 2x)`
Solution
`sqrt(1 - sin 2x) = sqrt(1 - 2sinx cos x)`
= `sqrt(sin^2x + cos^2x - 2sinx cosx)`
= `sqrt((cosx - sin x)^2`
= `cos x - sin x`
So `int sqrt(1 - sin 2x) "d"x = int cos x "d"x - int sin x + "c"`
= `sin x - (- cos x) + "c"`
= `sin x+ cosx + "c"`
`sqrt(sin^2x + cos^2x - 2sinx cosx) = sqrt((sinx - cosx)^2)`
= `sin x - cos x`
So `int sqrt(1 - sin^2x) "d"x = int sin x "d"x - int cos x "d"x + "c"`
= `- cos x - sinx + "c"`
= `- (cos x + sin x) + "c"`
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