00:01
So what i would do in this problem is draw out y equals 7 square root of x, but then also draw out 7x cubed.
00:16
And since we're revolving around the x -axis and this is the region that we're looking at, what i'm thinking about doing is the washer method, because you definitely have this empty space between the two points of intersection.
00:30
Now, i don't know if it's obvious, but the two points of intersection aren't zero.
00:34
And if you plug in 1 in for both those xes, you will get 7.
00:39
There's a lot of calculus problems that do 0 and 1.
00:42
So that kind of gives that away.
00:44
So the volume is going to be pi, the integral from 0 to 1, of the upper function, which is that 7 root x being squared.
00:55
And then you want to subtract off the lower function of 7x cubed squared in terms of x.
01:02
So just to do a little bit of simplification, you do have to square the 7 and the squared of x.
01:10
So 7 squared is 49, root x squared is x, and then 49 multiplying these exponents gives you x to the 6...