Question

Find the volume of the region bounded in back by the plane x=0 , on the front
and sides by the parabolic cylinder x=1−y2 , on top by the paraboloid z=x2+y2 , and on the
bottom by the xy-plane. Find the volume of the region bounded in back by the plane x=0 , on the front
and sides by the parabolic cylinder x=1−y2 , on top by the paraboloid z=x2+y2 , and on the
bottom by the xy-plane. @Mathematics

Answer 1

do you have to integrate or just set up?

Answer 2

the only thing that i am having touble with is finding out what the top bound for radius in polar coordinates
thats all i need

Answer 3

then i can do the rest

Answer 4

I wouldn't do polar. You will have to break it up

Answer 5

no you wouldnt. you never have to break things up in polar. thats only in Cartesian

Answer 6

well the radius is defined as two different functions at different points. I've never heard of a way to do that in one go.

Answer 7

thats if you convert it from y as a function of x to x as a function of y

Answer 8

\[\int\limits_{-\pi/2}^{\pi/2}\int\limits_{0}^{?}\int\limits_{0}^{r^2}\]

Answer 9

all i need is the top bound

Answer 10

are you trying to use cylindrical coordinates of a non cylinder?

Answer 11

should be rdrd(theta) times a height z or dz

Answer 12

yeah thats what that integral is up there

Answer 13

i just need to know top R

Answer 14

a varying r turns it into spherical coordinates which is a different ballgame in this case. when you hit the parabaloid up top, the far radius changes

Answer 15

no thats circular. The R is taken from the shadow cast on the xy field