00:01
I want to find the volume that's enclosed by the curve, y equals minus x squared plus 3x plus 4, which is this parabola.
00:09
I know that she gave me a picture, but i went ahead and completed the square in case i needed any of this information.
00:17
Okay, so it's an upside -down parabola.
00:19
It's for x is three halves, 25 -fourths.
00:23
It's y intercept is 4.
00:25
It's x -intercept is 4.
00:27
And then this line, x plus y equals 4, which has the same.
00:32
Intercepts.
00:32
Okay, we're going to send that around the y -axis and so we want to cut vertically, oops, because we're making shells, so we'll just cut like this.
00:43
And notice that no matter which one i draw, they all have the same curve on the top, which is the parabola and the same curve on the bottom, which is the line.
00:54
So that's a good thing.
00:56
Okay, so here's the shell.
00:57
Oops.
01:09
All right.
01:10
Okay, pretend like here's the shell.
01:13
Okay, volume of a shell is 2 pi r -h -t, or h is the height.
01:23
R is the radius from the center, the axis of rotation, out to somewhere in the shell.
01:35
And then t is the thickness of the shell.
01:37
And so t here is dx.
01:42
So rht, t is dx...