Question: Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by
and
. Find V both by slicing and by cylindrical shells. In both cases, draw a diagram to explain your method.
My work:
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a) Volume by slices.
Since this is rotated about the y-axis, I solved in terms of x:
Then I said the cross-sectional areal will be
since x will be the radius.
So I plugged my equations into it:
Since they intersect at the points (0,0) and (1,1) Volume will be from y=0 to y=1:
[snip]