Let R be the region in the first quadrant bounded by all three of the curves x = 2, y = 1, and y = (x−4)^2.
Compute the volumes V1, V2, and V3 of the solids of revolution obtained by revolving R about the x-axis, the y-axis, and the x = 5 line, respectively.
FIRST, I am trying to conceptualize this problem. I have the 3 necessary curves graphed. A 'triangle' looking figure is formed between y=1 to 4 and x =2 to 3. Do I need to find the volume of THIS figure revolved around the various axis points OR do I need to find the volume between y=0 to 1 and x = 2 to 4.
Both areas are bounded by all 3 curves. My intuition tells me to take the volume of the 'triangle' looking figure, but I did not want to proceed until I figured this part out.