Disk and washer method

1. Aug 11, 2011

chupe

Consider the region bounded by the curves y=x^2+1 and y=3-x^2

a) using the disk/washer method, find the volume of the solid obtained by rotating this region about the x axis

This was very straight forward
v=int(1, -1) pi((3-x^2)^2)-(x^2+1)^2))dx
I finished the problem with 32pi/3 which I think is correct.

However the next part I have no idea how to set up using the disk washer method.

b) Set up the integral for finding the volume of the solid obtained by rotating about the y-axis.

I know that the integration will have to be done in parts but I don't know where to split it into parts. If someone could help me set up the question that would be amazing.

Thank you,
Cheers

2. Aug 11, 2011

HallsofIvy

the second part looks much simpler than the first! You have already determined, for the first part, that the two graphs intersect at x= -1 and 1. Those are, of course, at $y= (-1)^2+ 1= (1)^2+ 1= 3- (-1)^2= 3- (1)^2= 2$. That is, you need to do y= 1 to 2 and y= 2 to 3 separately.

Last edited by a moderator: Aug 11, 2011
3. Aug 11, 2011

SammyS

Staff Emeritus
More like y= 1 to 2 and y= 2 to 3. (Oh! HoF already corrected this.)

Also, if you do the disk/washer method, only include the part of the region for x ≥ 0 , or x ≤ 0, otherwise you will have twice the actual volume.