Suppose that a curve is given in polar coordinates by an equation of the form r = f (θ),...

Suppose that a curve is given in polar coordinates by an equation of the form r = f (θ), where f is of class

C ¹. Use Definition 2.1 to derive the formula

for the length of the curve between the points ( f (α), α) and ( f (β), β) (given in polar coordinates).