00:01
So what makes this problem a little bit tricky is they don't tell you the bounds.
00:05
But if you were to look at f of x, which is defined as x squared plus 2x, and you just do a little, like the y intercept is clearly zero.
00:18
It's an upwards parabola.
00:20
If you were to factor out, you get x equals negative 2 as another zero.
00:25
I'm assuming you're familiar with a lot of tricks with algebra.
00:31
To get these values.
00:34
And then as well as g of x, i'll do this in blue, is the line, x plus 2.
00:42
So it has a y intercept at 2.
00:44
And then it goes up one, right one.
00:48
So it kind of looks like this, up one, right one.
00:51
So it's pretty clear to me that there's one point of intersection, because we have to do our bounds from negative 2 to some positive number.
01:01
I'll find that in a second.
01:03
And then you want to do your upper function, which is that x plus 2.
01:08
And then you have to subtract off the lower function, which is that x squared plus 2x.
01:16
So as i mentioned, you have to find these points of intersection.
01:21
And you can do that by setting them equal to each other.
01:24
X squared plus 2x is equal to x plus 2.
01:27
So what i would do is subtract this 1x over here.
01:33
So it would be 1x, and then subtract 2 to the left side.
01:38
And then you could factor out.
01:40
It'll be factors of negative 2.
01:42
That add to be 1 would be positive 2 and negative 1.
01:47
So then you can use the zero product property to see that x would be negative 2 or x equals positive 1.
01:53
So there's your bounds.
01:57
But i would also suggest to my students to simplify that because you want to distribute that minus in there.
02:04
So it would be negative x squared...