i am trying to make up my own equations for shell method and completely forgot how to do them. because we did them earlier in the year and have relied mainly on disc method.

My original function will be y=x^2. i have to include revolving around the x-axis, y-axis, x=a, and y=a and have to use the same example with each method. i have came up with

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

*integral for first two will be from 0 to 2 and for the last 2 will be from 0 to 4

*i am not sure if they will even work because i am having to make up my example

what would be the p(x)h(x) or p(y)h(y) for each of those?