00:01
Okay, so we've been asked to use the line integral to compute the area of the region bounded by y equals x squared, which is a screen function, and y equals four, which is this horizontal upper bound.
00:18
So this region is going to be, the region they're referring to is all this here.
00:27
So what we're looking at, what we would normally do to do an integral would be to integrate over the x -axis.
00:39
And we can see that those points are here because negative 2 -4 and 2 -4 is on that line.
00:45
So this would be negative 2, negative 1 -1 -2.
00:47
So over the horizontal axis, it would be negative 2 -2 to 2.
00:52
But that's not going to give us the area that we want because of this upper bound.
00:56
The area we're looking for is up here, not this lower area underneath the curve.
01:04
So what we need to do now is integrate with respect to y.
01:11
Okay, so now that we've established that y is the upper boundary, this is going to be what we integrate over from y value zero here to four.
01:22
So then we're going to use this equation of the parabola, to integrate over.
01:30
However, we need to make this equation in terms of x in order to integrate with respect to y...