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Numerade Educator

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Problem 7 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.

$ x = \sqrt{y} - y $, $ 1 \le y \le 4 $

Answer

$L=\int_{1}^{4} \sqrt{1+\left(\frac{1}{2 \sqrt{y}}-1\right)^{2}} d y \approx 3.6095$

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Video Transcript

Hey, it's Claire. So when you right here. So we have X is equal to squirt of wine minus wine. You know why it's between one and four included. So when we take the derivative, we get one over two square root of why minus one. So our art length using our formula get from 1 to 4 square re, uh, by one less one over two square root of why minus one square. Do you, I And this gives us around 3.6 095