★ calc ; unit 8 formulas

A = ∫_a^b[ f(x) - g(x) ] dx

the area between two curves

V = ∫_a^b[ s² ]dx ; where s = f(x) - g(x)

square cross sections

V = ∫_a^b[ width - height ]dx ; where width = f(x) - g(x), height is given

rectangle cross sections

V = ∫_a^b[ √3/4 * s² ]dx ; where s = f(x) - g(x)

equilateral triangle cross sections

V = ∫_a^b[ ½ * s² ]dx ; where s = f(x) - g(x)

isoceles right triangle cross section

V = ∫_a^b[ ½ * π r² ]dx ; where r = ( f(x) - g(x) ) / 2

semicircles cross sections

V = ∫_a^b π [ R(x)²]dx

volume of a solid of revolution

V = π ∫_a^b [ 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)