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  • 4 years ago

Calculus II - Arc Length Just wanted to verify my work and see if anything could be done more easily. Find the exact arc length of the portion of the graph of \[y = (1/6)x^3 + 1/(2x) \] from x = 1 to x=2 dy/dx = \[(x^2/2) - (1/(2x^2))\] \[(dy/dx)^2 = x^4/4 + (1)/(4x^4) - 1/2 \] \[(dy/dx)^2+1 = x^4/4 + (1)/(4x^4) + 1/2 \] \[\int\limits_{1}^{2}\sqrt{x^4/4 + 1/(4x^4) + 1/2}\] Arc Length = 17/12

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  1. anonymous
    • 4 years ago
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    My biggest question is 1) Whether the answer is right and 2) Whether it is possible to get a perfect square from (dy/dx)^2 + 1, since the integral of that was an absolute nightmare.

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