see here

i will use the shell method for all. all integrals will be written in the form:

y=x^2, y=0, x=2 revolve around y-axis

y=x^2, y=0, x=2 revolve around x= 3

x= sqr(y), y=0, x=2 revolve around x-axis

x= sqr(y), y=0, , x=2 revolve around y= 4

be sure that you can identify what i used for the radius when we are not going about either of the axis. in the shell method, there are only 3 forms for the radius, and it does not depend on the function. you can memorize them. (they make sense, so you can figure them out too. so make sure you know them)