Triple Integrals

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9 Terms

1
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Volume

∫∫∫SdV

2
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Average Value

1/V * ∫∫∫Sf(x,y,z) dV

3
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Mass of solid with density

∫∫∫Sδ(x,y,z) dV

4
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centroid of a solid

xA = (∫∫∫S x dV) / V; repeat for y and z

5
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Center of Mass with density

xM = (∫∫∫S xδ(x,y,z) dV) / M

6
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Moment of Inertia

relationship between angular acceleration and torque; mass/velocity * ∫∫∫(distance to axis)² dV

7
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triple integrals geometrically

“adding up” a function over every point in a solid

8
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Volume of a Solid bounds

outside integral → constant; middle bounds → only include remaining variable; inside integral → can include two other variables

9
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how do you find bounds (upper/lower)?

plug in point with the two variable coordinates (not the variable you’re finding the bounds for) that is inside the intersection