00:01
Find the area under the curve of these two functions.
00:05
So first i want to do is find the boundary.
00:07
Where are we going to integrate from? so i'm going to substitute x for y and get x equals 5x minus x squared.
00:15
So when i subtract x, i'm going to get 0 equals 4x minus x squared.
00:21
I'm going to factor out that x, 4 minus x.
00:24
So i get x equals 0 and x equals 4 as my boundaries.
00:28
That's what we're going to use when we integrate.
00:30
So we'll go ahead and put that in there.
00:32
So we also need to know which graph we're going to subtract from the other.
00:37
So when i do a quick graph sketch of this, from 0 to 4, i know that that's where they're going to intersect.
00:43
So i know at 1, this is going to be at the point 1 -1.
00:47
When i put 1 in place of x here, i'm going to get 5 minus 1, which is 4.
00:53
So that means that's going to be above.
00:55
So we're looking at the curved graph being above the line.
01:00
So this is what we want to integrate.
01:02
So we're going to take this y and subtract this y...