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Length of a Parameterized Wire

Multivariable calculus warmup

Find the length of a wire with parameterization \(\mathbf{r}(t) = \langle 3t + 1, 4 - 2t, 5 + 2t \rangle, 0 \le t \le 4.\)
arc-lengthparametric-equationsvector-functionsintegrationconstant-speedmultivariable-calculuscalculus-iiilength-of-curvevector-calculusline-segmentdefinite-integralthree-dimensional-geometry

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What you need first

What this problem tests

Tests the ability to differentiate a vector function, compute its magnitude, and evaluate a simple definite integral.

This is a standard introductory problem in multivariable calculus for computing the arc length of a space curve.

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