00:01
Okay, so in this video we're given the field f, which is just y, comma, negative x.
00:07
And we're asked to determine the line integral along the curve.
00:10
Our curve is a circle of radius 3 centered at the origin.
00:15
And the first thing we're going to try to do is parameterize this curve.
00:19
So this is pretty simple because we know that we're not a parameterized circle.
00:24
So since the circle has a radius 3, the x is just 3 cosine t, and the y is 3 .3.
00:30
Sine t or our t ranges from zero to two now what we're going to do is we're going to take the derivative with respect to t of x and y so the derivative of three cosine t is just negative three sine t the derivative of three sine t is just three cosine now we're going to determine the integral along the curve of f dot d r well that's basically the integral from zero to two pi because now we're taking the derivative at the integral with respect to t so we yeah so with respect to t so our limits are from 0 to 2 pi f of r of t dotted with r prime of t dd so we see that our f is given in terms of x and y so now we have to parameterize our field with x being 3 cosine t and our y being 3 so if we plug that in, we get 3 sine t comma negative 3 cosine t.
01:33
And our r prime of t is just negative 3 sine t comma 3 cosine.
01:38
Now we take the dot product, so we get negative 9 sine squared minus 9 cosine square...