Integral calculus - volumes of revolution?

Question

I understand how to calculate areas under curves using integrals.. but now I am totally lost with calculating volumes. Is there one formula that always works, or do you always have to look at each problem separately. For example, does it always work do just find the area of a cross section and integrate it?

Answer 1

See the web sites below.

Answer 2

If you know the cross sectional area of a solid , then you can find the volume by V = integral from a to b[A(x)dx, where A(x) is the cross sectional area of the solid at a distance x from a fixed point.

But the most used method of computing volumes is by rotating a
plane figure about an axis. For example ritating a right triangle about a vertical or horizontal axis gets you the volume of a cone.
This uses the method of cylindrical disks , or cylindrical washers or cylindrical shells.

Answer 3

ah ah carry on at the same time as I pull out my calc education guide Plug contained in the values and compute for V= pi* the anti-by-product of (distance of axis of rotation to Y=0)^2 -(function of the outlines of the shape in question)-(axis of rotation) this mind-set to searching the quantity of a rotating sturdy is named the washing device technique and please PLEASE enable me understand if I wrote it properly why did not you purely pay interest in college -_-