00:01
The arc length of y equals 1 8 x to the 4th plus 1 over 4x squared on 1 2.
00:07
So this is the same as y equals 1 8th, x to the 4th plus 1 4th, x to the minus 2.
00:16
So remember the arc length formula here will be 1st x to 2nd x, square root of 1 plus y prime squared the x.
00:26
So y prime is going to be one half x cubed minus one half x to minus three.
00:38
I'll factor the one half out there.
00:44
Next i need to square that.
00:47
So get one fourth, x to the sixth, minus one, minus one, plus x to the minus six, or one fourth, x to the 6 minus 2 plus x to the minus 6.
01:11
Then i'm going to add 1 to that.
01:15
So we got 1 plus 1 4th, x to the 6 minus 1 1 1ā2 plus 1 4th, x to the 6.
01:24
So this positive 1 and this minus 1ā2 makes a positive 1ā2.
01:36
Okay, and so if i factor the 1 4th out, i get x to the 6 plus 2 plus x to the minus 6.
01:44
Which you can see looks exactly like that, except for instead of a minus, it has a plus...