(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the arc length of the following curves on the given interval by integrating with respect to x

y=x^4/4+ 1/(8x^2); [1,2]

2. Relevant equations

Let f have a continuous first derivative on the interval [a,b]. The length of the curve from (a,f(a)) to (b,f(b)) is

L = integral[a,b] sqrt(1+f'(x)^2) dx

3. The attempt at a solution

y=x^4/4+ 1/(8x^2); [1,2]

I took the derivative and got

dy/dx = x^3 - 1/(4x^4)

I than square this and got

x^6 - 1/2 + 1/(16*x^6)

plunging into the formula I get

integral[1,2] sqrt(1/2 + x^6 + 1/(16*x^6)) dx

I have no idea were to go from here. I tried making several substitutions and than realized that there was nothing in my techniques of integration to evaluate this in any way or form. I plugged the indefinite integral into wolfram alpha to see what it got for the antiderivative and apparently it doesn't know how to integrate this neither.

http://www.wolframalpha.com/input/?i=integral+sqrt%281%2F2%2Bx^6%2B1%2F%2816x^6%29%29

well apparently it came up with a antiderivative it just has no steps to prove it to be correct when you click on show steps "(step-by-step results unavailable)". So I conclude that there is something really simple that I'm not seeing or something really complicated. This came from my textbook in -Applications of Integration-Lengths of Curves

Thanks for any help!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Calculus II - Lengths of Curves - Hard

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