Explain why, when a smooth planar curve is written in the form , the derivative that…

MATHEMATICS · Subjective · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

Explain why, when a smooth planar curve is written in the form

x=g(y)

, the derivative that appears inside the arc-length integrand must be

\dfrac{dx}{dy}

rather than

\dfrac{dy}{dx}