Figure 5.4.4(a) shows the  tutor applied to finding the arc length of $\sin \left(x^2\right)$ on the interval $\left[0\,2\right]$.

In the graph, the function is in red; the integrand, in blue; and the arc-length function, in green.

Although an arc-length function exists, its rule can't be expressed analytically without an antiderivative for the arc-length integral. However, the tutor numerically evaluates the integral at enough points for a graph of this function to be drawn.

Tools≻Load Package: Student Calculus 1

Apply the ArcLength command with the output option set to integral.

Press the Enter key to obtain the unevaluated arc-length integral.

Context Panel: Approximate≻10 (digits)