Find the equation of the curve that passes through the point (x, y) = (0, 1) and has an arc length on the interval given by the integral

Question

Find the equation of the curve that passes through the point (x, y) = (0, 1) and has an arc length on the interval  given by the integral  

	y = tan(x)
	y = tan-1(x)
	y = sec(x)tan(x)
	y = sec(x)

Answer 1

y' = secxtanx; y = ∫secxtanxdx = secx + C;

y(0) = sec0 + C = 1; C = 0

So, y = secx