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ggrree

  • 4 years ago

What is the arclength from x=0 to x=9 of this curve: y=1/3 (√x)(x−3) I can get most of the way there, but I run into mechanical problems when I try to actually evaluate the integral

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  1. dumbcow
    • 4 years ago
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    \[Arc length = \int\limits_{0}^{9}\sqrt{1+f'(x)^{2}}dx\] \[f'(x) = \frac{x-3}{6\sqrt{x}}+\frac{\sqrt{x}}{3} = \frac{x-1}{2\sqrt{x}}\] \[\rightarrow \int\limits_{0}^{9}\frac{x+1}{2\sqrt{x}}dx\] \[= \frac{1}{2}\int\limits_{0}^{9}(x^{1/2}+x^{-1/2})dx\] \[=\frac{1}{3}x^{3/2}+x^{1/2} from 0->9\] \[=12\]

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