# How do you find the arc length of the curve #y = (x^4/8) + (1/4x^2) # from [1, 2]?

##### 1 Answer

If you don't remember the arc length formula, you can use the distance formula:

This is just a "dynamic", infinitesimally-short-distance formula that accumulates over an interval of constantly increasing

So, first let's take the derivative and square it.

Now you can insert this as:

Cross-multiply:

Factor out

Now I want to somehow get this into a perfect square under a square root if possible. This was:

...and as it turns out, **there is no answer in terms of standard mathematical functions**, so we have to stop writing here.

All you can do is *numerically* evaluate this on your calculator or Wolfram Alpha, so if it weren't for the boundaries, this would not be that fun!

The numerical result is

graph{(y - x^4/8 - x^2/4)*sqrt(1^2 - (x-1)^2)/sqrt(0.5^2 - (x-1.5)^2) = 0 [-2.92, 5.85, -0.955, 3.428]}