Shift the coordinate axes by 2 units upward then it is the same as about y-axis

Thus,

integral^1_0 pi [x(1-x)-2]^2dx

Shift the coordinate axes by 2 units to the right, thus, x becomes x-2, which as the same as the area bout x-axisOriginally Posted byMoneyTree

Thus,

2pi*integral_2^3 x[(x-1)(-x)] dx

Note the change in the limits on integration because I made a shift.