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# Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.$y = x - \ln x$, $1 \le x \le 4$

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

#### Topics

Applications of Integration

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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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

#### Topics

Applications of Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp