00:01
I want to find the area of the region enclosed by the given curves.
00:08
And for that, we want to draw the curves.
00:10
So let's solve y is equal to negative 4x to the 4th plus 4.
00:18
And this one has y is equal to x to the 4th minus 1.
00:27
So graphically, let's be just a sketch.
00:31
So this is at plus 4 opening down.
00:38
And this one is at minus 1.
00:41
Opening up.
00:44
Okay, so this one is y is equal to x to the fourth minus one.
00:50
This one is y is equal to negative four x squared plus four.
00:55
So this was a square.
01:00
Okay, and we want to know what is this area.
01:02
Okay, so to integrate that, i need to know what are the x coordinates of the intersections.
01:07
Okay, so we set them equal to each other and solve.
01:10
So it's negative four x squared plus four is equal to x to the fourth minus one.
01:17
0 is equal to x to the fourth plus 4x squared.
01:21
Subtracking the 4 over, you get minus 5.
01:25
Okay, so this is going to be x squared and x squared...