00:01
Okay, here i want to find the arc length along this curve from y equals 0 to y equals 9.
00:06
Well, the arc length formula is this.
00:11
This will be the integral between 0 and 9 and then the square root of 1 plus dx by d .y, this squared.
00:28
This formula you can find in all formula sheets, dx, of course.
00:33
At the end.
00:36
So first step then is find dx by d y.
00:39
So from here then we have x equals negative 4 y power 3 over 2.
00:49
So d x by d y will be negative 6 y to the power of 1 half, which means if i square this d x by d y all squared i get 36.
01:07
Which means then my arc length i want to find is the integral 0 to 9 square root of 1 plus 36 y d .y.
01:25
Now this is integral 0 to 9 36y plus 1 power of 1 half and this i can do by reverse differentiation.
01:41
I know it's going to be 30 6 y plus 1 to the power of 3 over 2.
01:48
Just add 1 to this power here.
01:52
Then by differentiation, i take this and differentiate it.
01:55
I'm going to get 3 over 2 in front...