I know how to find the arc length of a curve but I keep gett

I know how to find the arc length of a curve, but I keep getting the answer wrong. I would appreciate if someone would go through the problem step-by-step so I can see where I am going wrong. Thank you so much.

Solution

Let\'s assume you\'re talking about the length of this curve over the entire domain of the function (0,1) {due to arcsin(sqrt(x))}. In that case... The length is determined by the integral of the square root of (dx^2 + dy^2) = ? sqrt (1 + [dy/dx]^2) dx dy/dx = (1 - 2x) (1/(2 sqrt(x-x^2))) + [1 /(2 sqrt(x))] (1 / sqrt(1-x)) = (1-2x)/(2 sqrt(x-x^2))) + 1 / (2 sqrt(x(1-x)) = [(1-2x) + 1] / (2 sqrt(x(1-x))) = (2-2x) / (2 sqrt(x(1-x)) = (1-x) / sqrt(x(1-x)) = sqrt((1-x)/x) = sqrt(1/x - 1) So the length of the curve is: L = ? sqrt(1 + 1/x - 1) dx = ? sqrt(1 + 1/x - 1) dx = ? 1/sqrt(x) dx = 2 sqrt(x) (from 1 to 0) = 2 - 0 = 2