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Find the exact length of the curve.

$ y = 1 + 6x^{\frac{3}{2}} $ , $ 0 \le x \le 1 $

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Video by Clarissa Noh

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Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 1

Arc Length

Applications of Integration

Missouri State University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

03:10

Find the exact length of t…

02:50

02:39

02:41

02:36

03:27

04:09

07:02

08:12

03:05

Graph the curve and find i…

03:13

06:02

Hey, it's Claire. So when you right here. So we have. Why is equal to one plus six x to the three hounds. When we differentiate this, we get d Y over D. X is equal to nine x to the one, huh? And using the art length formula we get l is equal to from 0 to 1 square e one plus nine x the 1/2 square d x this is equal to from 0 to 1 square root of one plus 81 x e x. We're gonna let you be equal to one plus 81 x So do you is equal to 81 d x. So this gives us well is equal to one over 81. And here we're gonna change the limits of integration. So a is equal to 82 and B is equal to one. So we put one 82 square root of you and then this gives us to over 243 Time 82 spirit of 82 minus one

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