00:01
Okay, so we're given this curve, which is actually a quarter of a circle in the first quadrant, and then we also have this vector field.
00:13
We want to calculate the flux across the curve.
00:19
You want to calculate this integral.
00:21
So what's going on here is that we have to dot the force into a vector that's perpendicular to our curve, the normal vector.
00:33
And so the curve, it goes x prime, y prime.
00:40
The vector x prime, y prime, that's the tangent.
00:44
We need the normal, and so it has to be perpendicular to that.
00:49
And so we get something that looks like this as our normal vector.
00:57
And it's not too surprising that that's the radial unit vector because that's the vector that's normal to our curve.
01:06
So if i write those out in terms of x and y, it looks like this.
01:18
Okay, now i want to write those in terms of my sines and cosines.
01:40
I'm writing it in terms of the double angle.
01:43
That makes it easier to integrate.
02:04
So the first term gives us pi over 2.
02:08
Second term gives us a half.
02:10
The integral of sine is the cosine divided by 2, evaluated from 0 to pi over 2...