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

A y = sin(x)

B y = cos(x)

C y = cos^-1(x)

D y = tan(x)

Question

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

A
y = sin(x)

B
y = cos(x)

C

y = cos-1(x)

D
y = tan(x)

Brandon B. · Accepted Answer

Arc length is ∫ds = ∫(dx2+dy2)1/2 = ∫(1 + dy2/dx2)1/2 dx. So we see that dy/dx = cosx ⇒ y = sinx + C. y(0) = 0 ⇒ C = 0.

Find the equation of the curve that passes through the point (x, y) = (0, 0) and has an arc length on the interval x is between 0 and pi over 4 inclusive given by the integral the integral fro...