Thread: Area & Volume Using Integrals

I can't get the answer which I think I'm supposed to be getting. Could someone please go through this so I'll understand it.

Sketch the area A defined by y = x(1-x) and the x-axis.
a) compute the volume when the area is revolved by the line y = -2.
b) compute volume when area is revolved about line x = -2


I am 99.9% positive that the volumes should be the same when you solve using both the x and y lines, but I am getting different answers. Please help!!!

Originally Posted by TreeMoney

I can't get the answer which I think I'm supposed to be getting. Could someone please go through this so I'll understand it.

Sketch the area A defined by y = x(1-x) and the x-axis.
a) compute the volume when the area is revolved by the line y = -2.

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

Originally Posted by MoneyTree

b) compute volume when area is revolved about line x = -2

Shift the coordinate axes by 2 units to the right, thus, x becomes x-2, which as the same as the area bout x-axis
Thus,
2pi*integral_2^3 x[(x-1)(-x)] dx
Note the change in the limits on integration because I made a shift.