Find Volume of Revolution for y=2+x and y=x^2 about y-axis | Shell Method

[miz_ai]

Homework Statement

Find the volume generated by rotating the area bounded by y=2+x and y=x^2 about the y-axis.

Homework Equations

Volume of revolution.

The Attempt at a Solution

shell method
integral (0 to 2) of x(2+x-x^2) dx

I think this can be solved by eliminating the left part and only count the volume of the left side, because the left part of the solid result is covered by the right part. It's a problem in my school because our teacher is debating whether the left part is counted or not.

i'm sorry i can't write in equotion.. I'm newbie

 

[HallsofIvy]

IF the problem really says "rotate around the y-axis, then you are right: the solid is generated is by the region between y= x+ 2 and y= x² for x> 0. The problem would make more sense and be more interesting if it were rotated around the x-axis.