Let R be the region in the first quadrant bounded by the graphs of y = 2x² (red), y = x(green), and the y-axis (see graph given). (a) Find the volume of the solid generated by revolving R about the y-axis using the shell method. Sketch the region together with an appropriately labeled representative strip. (b) Find the volume of the solid generated by revolving R about the x-axis using the washer method. Sketch the region together with an appropriately labeled representative strip.

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