For a smooth curve given by with continuous on

MATHEMATICS · Single correct · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

For a smooth curve given by

y=f(x)

with

f'(x)

continuous on

[a,b]

, which expression represents an infinitesimal element of arc length along the curve? (a)

ds=\sqrt{1+\left(\dfrac{dx}{dy}\right)^2}\,dx

(b)

ds=\bigl(1+\left(\dfrac{dy}{dx}\right)^2\bigr)\,dx

(c)

ds=\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}\,dx

(d)

ds=\left|\dfrac{dy}{dx}\right|\,dx