The  tutor shown in Figure 5.4.2(a) applies only to functions $f\left(x\right)$. Hence, to find arc length for $x\=y^2$, the tutor must be called with $y\=\sqrt{x}$.

As in Figure 5.4.1(a), the red curve is a graph of the function; the blue curve, the integrand; and the green, the arc-length function.

The keen observer will see that the forms of the exact value of the arc length given by the tutor and by direct integration in the Mathematical Solution, are not the same. But they are equivalent, as the numerical approximations suggest.

Tools≻Load Package: Student Calculus 1

Apply the ArcLength command, including the option to return the inert integral.
Context Panel: Evaluate and Display Inline
Context Panel: Evaluate Integral