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Numerade Educator

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Problem 8 Easy Difficulty

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

$ y^2 = \ln x $, $ -1 \le y \le 1 $

Answer

$L \approx 4.2552$

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Video Transcript

we have to find the length of the curve y squared equals Ln x on the interval. Why is greater than or equal to your negative one, but less under equal to one so we can rearrange why it's where equals Alan X. By raising both sides to E. This will give us X equals e to the wise Square. Then we'll want to find X prime to plug into our Ark formula equation. This is simply too. Why Times e two, the Y squared, plugging into our formula. Negative one for a and one for B one plus to Y E y squared squared again D y. If we plug this into our calculator, we should get around 4.2552