Find The Exact Length Of The Curve. X = Y4 8 + 1 4y2 , 1 ≤ Y ≤ 2

find the exact length of the curve,

`x=(1/8)y^4+1/(4y^2)`

`1<=y<=2`

please explain as thorough as possible

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We will use one of the formulas for arc length:

`int_a^b sqrt(1+(dx/dy)^2) dy`

`x=(1/8)y^4+(1/4)y^(-2)`

`dx/dy = (1/2)y^3-(1/2)y^(-3)`

`(dx/dy)^2 = (1/4)y^6 - (1/2) + (1/4)y^(-6)`

`1+(dx/dy)^2 = (1/4)y^6 + 1/2 +...

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