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.
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