# How do you find the arc length of the curve y = 2 − x^2 from [0,1]?

It is given by the integral $L = {\int}_{0}^{1} \sqrt{1 + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^{2}} \mathrm{dx}$
Hence $\frac{\mathrm{dy}}{\mathrm{dx}} = - 2 x$ we have that
$L = {\int}_{0}^{1} \sqrt{1 + 4 {x}^{2}} \mathrm{dx}$