`y = x^4/8 + 1/(4x^2) , [1, 3]` Find the arc length of the graph of the function over the indicated interval.

Expert Answers

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Arc length (L) of the function y=f(x) on the interval [a,b] is given by the formula,

`L=int_a^b sqrt(1+(dy/dx)^2)dx` , if y=f(x) a `<=`  x `<=`  b,

Now `y=x^4/8+1/(4x^2)`

Now we need to differentiate the above function with respect to x,





Now arc length L=`int_1^3 sqrt(1+((x^6-1)/(2x^3))^2)dx`


















So, the Arc length=`92/9`


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