Calculus Questions - please don't provide final answer - only method of solving

30.Each integral represents the volume of a solid. Describe the solid. 2pi (integral TOP: 2 to BOTTOM: 0) [y/1 + y^2] dy

I assume you mean y / (1 + y^2)
y / (1 + y^2) = (1/2) * (2y)/(1 + y^2)
Let 1 + y^2 = u
Integrate and plug the limits.

1/2{2y/(1+y^2)}
since differention of bottom is equal to numerator then integration is log of the denominator
1/2{log(1+y^2) +C
Taking limits
1/2*{log(1+4) -log(1)}
1/2*{log(5)}
Volume = 2pi{1/2*log(5)}
= pi*log(5) ................Ans