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Numerade Educator

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Problem 5 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 = x - \ln x $, $ 1 \le x \le 4 $

Answer

$L=\int_{1}^{4} \sqrt{1+(1-1 / x)^{2}} d x \approx 3.4467$

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Video Transcript

he s Clearasil immune right here. So we have. Why is equal to X minus? Felt then of X exists between one and four included. When we find the derivative, we get one minus one over ETS. We're gonna use the arc length formula when we get from 1 to 4 square root, but one plus one minus one over at square D X. And when we used a calculator, we get around three point 4467