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Find the exact length of the curve.
$ y = 1 + 6x^{\frac{3}{2}} $ , $ 0 \le x \le 1 $
$\frac{2}{243}(82 \sqrt{82}-1)$
Calculus 2 / BC
Chapter 8
Further Applications of Integration
Section 1
Arc Length
Applications of Integration
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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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