Question

in solids of revolution if we rotate about x-axis should we write y=f(x) and about y-axis inform of x=f(y)

Answer 1

These revolutions will lead to The 'Disc Method' to determine volume. You 'should' rearrange for these forms (y = f(x)) if the function is easiest to integrate. otherwise you can use the 'Shell Method', but it will vary function to function as to which is the easiest method.