00:01
For this problem, we want to approximate the volume of the solid that is formed by rotating the region, banded by y equals cosine of x on the close interval 0 to 5 or 6, about the y -axis using simpson's rule for n equal to 8.
00:14
So first we want to draw the given problem.
00:17
We draw the region bounded by y equals cosine of x on the close interval 0 to 5 or 6, and then we indicate the x's of rotation.
00:27
So here is the graph of the solid.
00:31
And the next we pick a strip that will represent this region.
00:35
Let's say we pick a vertical strip.
00:38
And then we will rotate this strip about the y -axis, and from there we will be able to form a cylinder.
00:45
His radius is equal to this distance, and its height is equal to the length of the strip.
00:53
So by the shell method, volume is equal to the integral from a to b of 2 pi times the radius times the height and then dx.
01:06
Based on this figure, the interval a to b will be the interval 0 to pi over 6...