Find the length of the curve?

Not quite. y=sqrt(16-x^2) so y^2=16-x^2, so x^2+y+2=16. That is the circle of radius 4 centered at the origin, so if y>=0 you have the upper half of the circle. Integrate if you want...I would use geometry. The length of the curve is half of the cirference of the circle, so you have L=2pi*r/2=pi*r=4pi.