Finding Volume of Region Inside Sphere and Cylinder in Cylindrical Coordinates

[E&H12]

Find the volume of the region inside both the sphere x^2+y^2+z^2= 4 and the cylinder (x-1)+y^2=1using cylindrical coordinates.

I was thinking the inner limits would go from +(2-r) to - (2-r)
the middle intervals would go from 0 to 1
and the outer limits 0 to 2pi

is my approach correct

 

[LCKurtz]

Find the volume of the region inside both the sphere x^2+y^2+z^2= 4 and the cylinder (x-1)+y^2=1


using cylindrical coordinates.

I was thinking the inner limits would go from +(2-r) to - (2-r)
the middle intervals would go from 0 to 1
and the outer limits 0 to 2pi

is my approach correct

1. Did you mean the cylinder $(x-1)^2 + y^2 = 1\,$? I am assuming so.
2. You have to tell us what your order of integration is. For example are you describing the limits for $dzdrd\theta\,$?
3.If so, notice that $\sqrt{4-r^2}\ne 2-r$
4. To get correct $r,\theta$ limits you need to find the polar equation of the cylinder and plot its trace in the xy plane. Your limits are wrong.