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Question
Find `int (dx)/sqrt(4x - x^2)`
Solution
Let I = `int (dx)/sqrt(4x - x^2)`
= `int (dx)/sqrt(-(x^2 - 4x))`
= `int (dx)/sqrt(-(x^2 - 4x + 2^2 - 2^2))`
= `int (dx)/sqrt(-(x - 2)^2 - 2^2)`
= `int (dx)/sqrt(2^2 - (x - 2)^2)`
= `sin^-1 ((x - 2)/2) + C` ...`[∵ int (dx)/sqrt(a^2 - x^2) = sin^-1 (x/a) + C]`
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