first, clear up the meaning of
x=2=2sqrty
If you mean
x = 2+2√y, then since the curve intersects y=9 at (8,9) we have as usual, two ways to solve it. Using shells of thickness dx,
v = ∫[0,8] 2πrh dx
where r = x and h = 9-y = 9-(x/2 - 1)^2
v = 2π∫[0,8] x(9-(x/2-1)^2) dx = 1024/3 π
Of course, you can also use discs of thickness dy, but you have to allow for the hole in the middle for x in [0,2].
v = ∫[0,1] π(R^2-r^2) dy + ∫[1,9] πr^2 dy
where R = 2+2√y and r = 2-2√y
and where r = x = 2+2√y
I'll let you check my math and verify that they are equal.
find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
x=2=2sqrty, x=0, y=9 about the y axis.
Is this the disk or shells method and how do I set this problem up?
1 answer
1 answer