00:01
So for this problem, we are going to be looking at ds.
00:06
We know that ds is equal to the square root of dx, dt, squared, plus d .ydt squared, a second derivative.
00:35
So these values squared.
00:37
And then we know that the x and the y correspond to t and t over 2.
00:45
According to the problem.
00:46
So x is t, y is t over two.
00:55
So what this ends up doing is this is just going to be a one squared and this is just going to be a one -half squared.
01:13
With that we have our ds, and it's going to ultimately end up equaling the square root of five over two.
01:32
The ds value, and then the line integral, it's going to be from zero to four, because that's the point we have, or the interval we have.
01:45
So from 0 to 4, we'll take the integral from 0 to 4, t times root 5 over 2 d...