Homework Help: Finding Arc Length

1. Jun 21, 2011

MHrtz

1. The problem statement, all variables and given/known data

Determine the arc length of the function on the given interval

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

The arc length formula

$\int$ (f'(x)2 + 1).5 dx

3. The attempt at a solution

I used the arc length formula but don't know where to go from here. Usually these problems can't be done unless a form of cancellation takes place and I can't seem to find it. Below is what I input in the formula but I can not figure out how to integrate this.

$\int$((y6 - 1)2/(2y3)) + 1))).5 dy

2. Jun 21, 2011

Staff: Mentor

It's helpful in this problem to use negative exponents instead of fractions.

(x')2 + 1 = (1/4)y6 - 1/2 + (1/4)y-6 + 1
= (1/4)y6 + 1/2 + (1/4)y-6

This turns out to be a perfect square, so you can readily take its square root.

3. Jun 21, 2011

MHrtz

I factored and then took the square root and came up with this:

(y^3)/2 + 1/2y^3

4. Jun 22, 2011

HallsofIvy

Yes, that is correct. Now integrate.