00:01
For this problem we want to find the area of the region bounded by the parabola, f of x as equal to 8x minus x squared, from x equals 0 to x equals 8.
00:11
Now this parabola has a vertex of 416.
00:15
To get this vertex, we have to use this formula.
00:18
And we also note that since the leading coefficient is negative, then the parabola is opening downwards.
00:26
Note that the intersection also between this function and the x -axis can be found by setting this function equal to 0, which means that we have 8x minus x squared equal 0.
00:41
Factor out the x, we have x times 8 minus x equal 0, which gives us x equals 0 and x equal to 8, which are the boundaries of the interval where the region is found.
00:55
So if you are to graph this region, it should look like this.
01:02
And this should be our shaded region...