00:01
So we want to find the volume of the solid generated by revolving the region, y is equal to the square root of cosine of x, bounded by x between 0 to pi half, and y is equal to 0, which is the graph we have drawn here.
00:24
So remember the first thing we want to do is write what formula we would like to use.
00:32
And since we're revolving around the x -axis, and what we want to do is use the formula, a to b of pi, and actually i'll just write the pie on the outside, pi, whatever our radius is squared, with respect to dx.
00:59
So let's go ahead and figure out what our radius should be, and then we can figure out our balance of integration after.
01:05
And actually, maybe one thing i should do, since this is supposed to be to pi half.
01:09
Let's go ahead and draw that little boundary right there.
01:14
So our radius, so i'm going to go from here to here, and then i need to rotate like so.
01:23
And so that radius r is really just the distance that we have here for our y output, which is just going to be the square root of cosine x.
01:34
So i just get r of that...