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A = ∫ab[ f(x) - g(x) ] dx
the area between two curves
V = ∫ab[ s2 ]dx ; where s = f(x) - g(x)
square cross sections
V = ∫ab[ width - height ]dx ; where width = f(x) - g(x), height is given
rectangle cross sections
V = ∫ab[ √3/4 * s2 ]dx ; where s = f(x) - g(x)
equilateral triangle cross sections
V = ∫ab[ ½ * s2 ]dx ; where s = f(x) - g(x)
isoceles right triangle cross section
V = ∫ab[ ½ * π r2 ]dx ; where r = ( f(x) - g(x) ) / 2
semicircles cross sections
V = ∫ab π [ R(x)2]dx
volume of a solid of revolution
V = π ∫ab [ R(x) ]2 - [ r(x) ]2 dx ; where R(x) to the radius outside of the object and r(x) is the radius to the inside of the object.
volume of a solid of revolution (washers)
Note 
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