00:01
All right, so this question wants us to find the area of the region enclosed by these two curves.
00:04
I've gone ahead and completed the square on the function f -fx, and g -of -x we can graph pretty easily.
00:10
So what i'm going to do are graph these two functions in these two colors and find their area.
00:15
So to do that, let's find the first one.
00:17
It's going to be up 67 -fourths and then to the left three halves.
00:21
So we're going to start it right here.
00:22
It looks like we'll get something like this.
00:25
The purple one is going to be plus one.
00:28
And it's just going to be stretched by a factor of two.
00:31
So it looks something like this and something like this.
00:34
This is the region we care about.
00:36
I wish you'd be that in a different color just to emphasize that it's this region here.
00:40
The formula to find the area between two curves is going to be, well, whatever this endpoint is right here, whatever those endpoints are.
00:49
And it's going to be the top function minus the bottom function.
00:52
The top one's the red one.
00:53
So it's x plus three halves squared plus 67 fourths.
00:57
Another way of writing that would just be to use the original function, which is what we'll do to make our lives easy.
01:01
So x squared plus 3x plus 19...