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.
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:
b) volume by shells
Using the initial equations, solved for y, volume will be the volume of - volume of . from x=0 to x=1.
So volume =
So either one or both of my ways are wrong >.<