00:01
On the arc length of y equals 3 halves x to the two -thirds on the interval 1 -8.
00:06
Okay, so remember the formula for arc length is the square root of 1 plus the derivative squared dx from the first x to the second x.
00:24
Okay, so first we're going to find the derivative, and the derivative of that is 3 halves times 2 thirds x.
00:34
To the minus one third or one over x to the one third.
00:42
Next we're going to square it.
00:45
You get one over x to the two thirds.
00:50
Now we're going to add one to it.
00:57
Okay, so right here i'm going to go ahead and get a common denominator.
01:00
So i get x to the two thirds plus one over x to the two thirds.
01:08
Okay, next we need the square root of that.
01:15
So we get x to the two thirds plus one under the square root and x to the one third on the bottom...