Intergration dx/sqrt 4x-x^2?

1 Answer
Ratnaker Mehta
May 21, 2018

# arcsin((x-2)/2)+C, or, arcsin(x/2-1)+C#.

Explanation:

Suppose that, #I=intdx/sqrt(4x-x^2)#.

#:. I=intdx/sqrt{4-4+4x-x^2}#,

#=intdx/sqrt{2^2-(x^2-4x+4)}#,

#=intdx/sqrt{2^2-(x-2)^2#.

Knowing that, #intdt/sqrt(a^2-t^2)=arcsin(t/a)+c#, we get,

# I=arcsin((x-2)/2)+C, or, arcsin(x/2-1)+C#.

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