★ calc ; unit 8 formulas

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8 Terms

1
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A = ab[ f(x) - g(x) ] dx

the area between two curves

2
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V = ∫ab[ s2 ]dx ; where s = f(x) - g(x)

square cross sections

3
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V = ∫ab[ width - height ]dx ; where width = f(x) - g(x), height is given

rectangle cross sections

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

equilateral triangle cross sections

5
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V = ∫ab[ ½ * s2 ]dx ; where s = f(x) - g(x)

isoceles right triangle cross section

6
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V = ∫ab[ ½ * π r2 ]dx ; where r = ( f(x) - g(x) ) / 2

semicircles cross sections

7
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V = ∫ab π [ R(x)2]dx

volume of a solid of revolution

8
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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)