Question

The region bounded by y=3/(1+x^2), y=0, x=0 and x=3 is rotated about the line x=3. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are:

Answer 1

v = ∫[0,3] 2πrh dx
where r=3-x and h=3/(1+x^2)

or, using discs,

v = ∫[0,3] π(R^2-r^2) dy
where R=3 and r=3-√(3/y - 1)

Answer 2

nice