Find the anti derivative of f'(x)=4/(1-x^2)^(1/2) when f(1/2)=1
The Attempt at a Solution
My problem is as follows: aren't f(x)=4arcsin(x)+c and f(x)=-4arcos(x)+c both perfectly good anti derivatives of f'(x)? In this case, if I plug f(x) in as 1 and x in as (1/2), in the first case I find c to be 1-(4pi)/6, and in the second case I get c to be 1+(4pi)/3. I MUST be wrong somewhere!
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