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MathCalculus

Find the Length of the Curve Over the Given Interval: y = (1/3)(x² − 2)^(3/2) on [2, 4]

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Question

For the following exercises, find the lengths of the functions of xx over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it.

  1. y=13(x2−2)3/2y=\frac{1}{3}\left(x^{2}-2\right)^{3/2} from x=2x=2 to x=4x=4

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Evidence boundary

This page works the curve published as exercise 174 in the OpenStax Calculus Volume 2 §2.4 exercise set, whose instruction is to find the length of the function of x over the given interval and to use technology when the integral cannot be evaluated exactly. The value 50/3 is the exact value of the integral in that statement; the decimal 16.667 is given only for scale. The page does not claim the problem comes from any other worksheet, textbook or answer key, and it does not treat the same family of curves over a different interval.