How to come up with the integral for the volume of the rotation of a region bounded by curves with reference to a vertical line?

Question

anonymous · Answer

I understand the process of rotating a region with the x-axis and other lines parallel to it, but I keep having trouble formulating the integral of the equation representing the volume whenever the rotation is in reference with the y-axis and its meridians.

anonymous · Answer

What I usually do in such case is that I integrate the function with respect to y

anonymous · Answer

The region is bounded by the curves of:$$y=x ^{2/3}$$$$y=0$$$$x=0$$The rotation is in reference with the y-axis

turingtest · Answer

draw the picture

anonymous · Answer

@TuringTest yes that's a very good idea :D

anonymous · Answer

It helps a lot

turingtest · Answer

thanks, it's the only one I ever use

anonymous · Answer

then you identify the crosssectional area

anonymous · Answer

|dw:1333616173853:dw| This a rough sketch of how the graphs should look