Question

Question #2de8a

Answer 1

I am assuming you mean the length of the arc along the given curve between `x=a` and `x=b` (for some arbitrary values `a` and `b`)

In general the arc length of a polynomial `f(x)` is given by:

`int_a^b sqrt(1 + f'(x)^2) dx`

For this specific example:
`f(x) (=y) = ((x^3)/24)+(2/x)`

`rarr f'(x) = x^2/8 - 2/(x^2)`

`f'(x)^2 = x^4/64 - 1/2 + 4/x^2`

`1 + f'(x)^2 = x^4/64 + 1/2 + 4/x^2`

`int_a^b sqrt(1 + f'(x)^2) dx = int_a^b (x^2/8 +2/x^2) dx`

which should be relatively straightforward (once values are established for `a` and `b`).