Section 13.3: Arc Length & Curvature

Use Theorem 10 to show that the curvature of a plane parametric curve \(x = f(t), y = g(t)\) is \[ \kappa = \frac{|\dot{x}\ddot{y} - \dot{y}\ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}} \] where the dots indicate derivatives with respect to t.