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Example: Computing the Length of a Curve

You can use quad or quadl to compute the length of a curve. Consider the curve parameterized by the equations

where t is an element of the range from 0 to 3 pi.

A three-dimensional plot of this curve is

The arc length formula says the length of the curve is the integral of the norm of the derivatives of the parameterized equations

The function hcurve computes the integrand

Integrate this function with a call to quad

The length of this curve is about 17.2.

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