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# Find the exact length of the curve.$x = \frac{1}{3} \sqrt{y} (y - 3)$ , $1 \le y \le 9$

## $\frac{32}{3}$

#### Topics

Applications of Integration

### Discussion

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

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### Video Transcript

Hey, it's Clearasil when you right here. So we have X is equal to 1/3 square root of why? Why minus three? And why is between one and nine included? We're gonna differentiate e d x over d line. Then we get 1/3 times one over two square root. If I terms lie minus three plus 1/3 time's square root of why and this becomes equal to why minus one over two square root of Why So when we put it into our our Klink equation, we get from 1 to 9 square root. Why minus one square over four y plus one, Do you? Why, you only put a cure? It goes from 129 square root of why square minus two. Why plus one plus for Why over for why do you I This is equal to from 1 to 9 square root of y square plus two y plus one over four. Why do you Why, When this becomes equal to from 1 to 9 square it of life plus a one square over for Why do you lie which is equal to 32 over three

#### Topics

Applications of Integration

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp