1. Dec 29, 2005

frozen7

The volume surrounded by y = x^2 , y=0, x=-2, x=-1 , revolved about y axis,by using cylindrical method.

The region is actually within x=-1 to -2 and it can actually same with x=1 to 2.

height = x^2

Is my assumption correct?

2. Dec 29, 2005

Fermat

Your radius should simply be x. With limits of: x = 1 to 2

You assumption about being able to use the region in the 1st quadrant is correct, yes.

3. Dec 29, 2005

frozen7

How come the radius should be x?

4. Dec 29, 2005

Fermat

The radius should be x because the radius of the cylinder is the distance from the origin.
The volume of revolution is about the y-axis, which passes through the origin. And you are finding the volumes of all the thin cylinders starting with cylinders with a radius of x = 1 to x= 2.

See here for a further treatment of the cylindrical method.

Last edited: Dec 30, 2005
5. Dec 30, 2005

frozen7

Something wrong with the link you have given.

6. Dec 30, 2005

Fermat

Sorry 'bout that. Forgot to add in the url.