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anonymous
 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
anonymous
 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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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0My 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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