Find arc length. y = [(x^4)/8] + 1/(4x^2) on the interval [1,2]
I can find the derivative and then square it. Afterward, I plug everything into the arc length formula but cannot break down the integral in a form that can be integrated. I also apply u-substitution but find myself not able to completely remove x from the integral. This is a complicated problem. Does it involve other tools of calculus beyond basic integration? What is the arc length?
I can find the derivative and then square it. Afterward, I plug everything into the arc length formula but cannot break down the integral in a form that can be integrated. I also apply u-substitution but find myself not able to completely remove x from the integral. This is a complicated problem. Does it involve other tools of calculus beyond basic integration? What is the arc length?
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y' = (1/2) x^3 - 1/2 (x^-3)
y'^2 = 1/4 x^6 - 1/2 + 1/4 x^-6
y'^2 + 1 = 1/4 x^6 + 1/2 + 1/4 x^-6
(y'^2 + 1)^.5 = 1/2 x^3 +1/2 x^-3
and that is easy to integrate.
y'^2 = 1/4 x^6 - 1/2 + 1/4 x^-6
y'^2 + 1 = 1/4 x^6 + 1/2 + 1/4 x^-6
(y'^2 + 1)^.5 = 1/2 x^3 +1/2 x^-3
and that is easy to integrate.