00:01
For this problem, we are asked to evaluate the line integral of x plus 4 root y, counterclockwise around the triangle with vertices 0 ,0 ,10, and 01.
00:11
So i'll just quickly sketch out what our path here is.
00:15
So we have 0 to 1 0 to 0, and we're going counterclockwise.
00:20
So it would be like this.
00:24
And i'll express our overall curve here, our overall path, as three different segments.
00:29
Oops, c1, c2, and c3.
00:33
Then, next step here will be to parameterize each one of those line segments.
00:38
I'll note ahead of time here that i'm parameterizing each one of these for t between 0 and 1.
00:44
So we'd have that we can parameterize c1 as r1 of t equals t0.
00:52
R2 of t then we can parameterize as 1 minus t, t, and r3 of t.
01:01
Can parameterize as 0 -1 -t -t using that then we would have that let's see here r1 prime of t will be 1 -0 and so we'd have let me give myself a little bit more room here we'd have that the magnitude of r1 prime is going to be 1 then for r2 you can see that r2 prime is going to be negative 1 -1 so the magnitude of r2 prime will be equal to the square root of 2...