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:

-------------------

**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]