Integrating surfaces and solids of revolution with ���wheels���
P(p) is the parameter range of P.

Sliders to set roots of polynomial f(p):

Scaling factor for polynomial f(p):

f(p) is the function to be revolved around axis.

Area of sector (of a circle) of angle a :

Area of an annular (flat ring) sector with outer radius r , innner radius s, and angle a:

Volume of a disk-sector of radius r, angle a, and thickness T:

Volume of the sector of a wheel of square cross-section with outer radius r , innner radius s, angle a, and thickness T :

The edges of a rectangle with left at l, bottom at b, width w and height h.
p is the drawing parameter.

Filling in the interior of the rectangle:
u is the horizontal and v is the vertical parameter.

Plots
Dots at minimum and maximum x-values:

Plot the curve on the xy plane:

Rotation around the x-axis by the angle a:

Rotate the curve:

The interiors of the rectangles, at start and rotated:
function(I,K*W,0,W,(K*W)^2,u,v),in(k,set(4,5,6,7,8,9,10))
function(R_x,n*degree)*function(I,K*W,0,W,(K*W)^2,u,v),in(k,set(4,5,6,7,8,9,10))

The width of the wheels:

The edges of the rectangles, at start:

The edges of the rectangles, rotated:

The surfaces swept out by the edges:

This file was created by Graphing Calculator 3.5.
Visit Pacific Tech to download the helper application to view and edit these equations live.