# 13.6 Notes - 1 1 = = = = = = y y x x z xy z#18 Application...

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Calculus III Section 13.6 – Triple Integrals and Applications Definition of Triple Integral If f is continuous over a bounded solid region Q, then the triple integral of f over Q is defined as i n i i i i Q V z y x f dV z y x f = ∫ ∫ ∫ = ) , , ( lim ) , , ( 1 0 provided the limit exists . The volume of the solid region Q is given by Volume of Q = ∫ ∫ ∫ Q dV Example: Set up the six different triple integrals to calculate the volume of the solid bounded by the plane 12 4 3 2 = + + z y x in the first octant.

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Example: Set up the triple integral to find the volume of the solid bounded by x y x z x z 2 , 0 , 0 , 9 2 = = = - = . (#14) Example: Use a triple integral to find the volume of the solid bounded by
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Unformatted text preview: 1 , , 1 , , , = = = = = = y y x x z xy z . (#18) Application of Triple Integrals Suppose you have a solid region Q whose density at (x, y, z) is given by the density function ρ . The center of mass of the region is given by ( 29 z y x , , where ∫ ∫ ∫ = Q dV z y x m ) , , ( = yz M ∫ ∫ ∫ Q dV z y x x ) , , ( = xz M ∫ ∫ ∫ Q dV z y x y ) , , ( = xy M ∫ ∫ ∫ Q dV z y x z ) , , ( and m M x yz = , m M y xz = and m M z xy =...
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## This note was uploaded on 01/13/2012 for the course MATH 2574 taught by Professor Pamelasatterfield during the Spring '12 term at NorthWest Arkansas Community College.

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13.6 Notes - 1 1 = = = = = = y y x x z xy z#18 Application...

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