Question

Find the equation of the curve that passes through the point (x, y) = (0, 0) and has an arc length on the interval 0⩽x⩽π/4 given by the integral from 0 to π/4 of√(1+cos^2x) dx.

a) y= sin(x) ------> My answer. Can you check for me, pleaseeee?
b) y= cos(x)
c) y= cos^-1 (x)
d) y= tan(x)

Answer 1

since arc length is ∫√(1+(y')^2) dx
y' = cosx
so, y = sinx
I agree.

of course, y = -sinx would also work, but that was not one of the choices ...