If the position-vector description of a curve is given by $\mathbf{R}\left(t\right)\=x\left(t\right) \mathbf{i}\+y\left(t\right) \mathbf{j}\+z\left(t\right) \mathbf{k}$, then $\stackrel{\.}{\mathbf{R}}\=\stackrel{\.}{x} \mathbf{i}\+\stackrel{\.}{y} \mathbf{j}\+\stackrel{\.}{z} \mathbf{k}$, where the over-dot notation represents differentiation with respect to $t$. Hence, the integrand in the arc-length integral for R is $\sqrt{{\stackrel{\.}{x}}^2\+{\stackrel{\.}{y}}^2\+{\stackrel{\.}{z}}^2}$ = $∥\stackrel{\.}{\mathbf{R}}∥$.

Figure 2.2.3(a) provides a graph of the given curve.

Tools≻Load Package: Student Multivariate Calculus

Enter R as per Table 1.1.1.

Context Panel: Assign to a Name≻R

Calculus palette: Definite integral template

Calculus palette: Differentiation operator

Context Panel: Evaluate and Display Inline

Install the Student MultivariateCalculus package.

Define the helix as the position vector R.

Apply the int, Norm, and diff commands.