Arc Length of a Parametric Curve

Question

Consider the graph of a parametric curve provided in the stimulus above. All of the following statements regarding the computation of its arc length are true, except:

Accepted Answer

The arc length can be computed without taking the square root of the sum of the squares of the derivatives of $$x(t)$$ and $$y(t)$$.

Answer

The limits of integration for computing the arc length correspond to the parameter values over which the curve is defined.

Answer

The arc length of the curve is given by $$\int_{a}^{b} \sqrt{(dx/dt)^2 + (dy/dt)^2}\, dt$$.

Answer

Both $$dx/dt$$ and $$dy/dt$$ are squared, summed, and then the square root of the result is integrated over the interval for $$t$$.