00:01
Let's begin by roughly sketching the bounded region.
00:04
So we have this graph, and then this region is bounded by the equation x equals y squared, and the equation y equals 3.
00:15
And we want to revolve region r about the x axis.
00:20
So let's begin by labeling each of these equations.
00:26
So let's label this equation right here, f of y.
00:34
And then there's also a y equals a x equals zero equation right here, and we can label that g of y.
00:48
And the reason why we're labeling these is because the equation x equals zero is considered the left bound of the region, and this equation right here, x equals y squared, is considered the right bound of the region.
01:02
So now that we know that, we know that f of y, so this equation right here is greater than or equal to g of y on the interval zero to three and that means zero is here and three is here and you can see this on a graph and so now we can fill out the equation for shell method so the volume is equal to two pi times the integral from zero to three and then we know that the radius is y and then the height is just the right bound so f of y minus the left bound, so g of y.
01:45
And that ends up being y squared minus zero...