# OpenStax Errata

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This integral is solved by a change of variables, and the solution contains a factor-of-ten error.

<math>J=\int_0^{50}\frac{vdv}{.001v^2+9.8}</math>

<math>\text{Let }u=.001v^2+9.8</math>

<math>du=.002\,vdv</math>

<math>vdv=\frac{du}{.002} = 5\times 10^2 du \;( \text{not }5\times 10^3)</math>

<math>J=\left(5\times 10^2\right)\int\frac{du}{u}=\left(5\times 10^2\right)
\left.\ln\left(.001v^2+9.8\right)\right|_0^{50}\approx 114\text{ m}</math>

The book's numerical value is correct, but one step in the equation is wrong. This error was pointed out to me by a student at Wright State University Lake Campus.--Guy vandegrift (talk) 17:56, 13 February 2018 (UTC)