# a. write and simplify the integral that gives the arc length of the curve on the given integral y=1/x (1,10)

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### 1 Answer

The arc length of a smooth curve f(x) on the interval [a,b] is given by:

`s=int_a^b sqrt(1+[f'(x)]^2)dx`

Here `f(x)=1/x ==> f'(x)=-1/x^2` so

`s=int_1^(10) sqrt(1+1/x^4)dx`

The approximation for s is `s~~9.153`

**The integral does not "simplify" in terms of the basic trigonometric, exponential, or polynomial functions.**