Triple_integrals_and_3D_Coordinates_9-15

Triple_integrals_and_3D_Coordinates_9-15 - Triple Integrals...

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1 Triple Integrals ± This unit is based on Sections 9.15 Chapter 9. ± All assigned readings and exercises are from the textbook ± Objectives : Make certain that you can define, and use in context, the terms, concepts and formulas listed below: Evaluate triple integrals in Cartesian Coordinates Express points, surfaces and volumes in cylindrical coordinates Express points, surfaces and volumes in spherical coordinates Evaluate triple integrals in cylindrical and spherical coordinates Evaluate physical characteristics of solids using triple integrals: volume, center of mass, moment of inertia, total charge, total energy stored in a region…etc. ± Reading : Read Section 9.15, pages 539-550. ± Exercises : Complete problems
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2 ∫∫∫ ∫∫∫ = D D dxdydz z y x f dV z y x f ) , , ( ) , , ( Triple Integrals in Cartesian Coordinates ± The integral of a function f(x,y,z) over a 3D object D, is given by ± The limits on the integration depend on the shape of the body D dV = dxdydz represents an element of volume
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3 Triple integrals : limits of integration ∫∫ ∫∫∫ = = = = = = = b x a x x g y x g y y x f z y x f z D dx dy dz z y x u dzdydx z y x u ) ( ) ( ) , ( ) , ( 2 1 2 1 ) , , ( ) , , ( ± Assuming we integrate with respect to z, then y, then x, the innermost limits may depend on the other two variables (x and y), the middle limits may depend on the outer variable (z), whereas the outer limits are constants.
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This note was uploaded on 05/08/2009 for the course AAE 580 taught by Professor Nnjkl during the Spring '09 term at Ohio State.

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Triple_integrals_and_3D_Coordinates_9-15 - Triple Integrals...

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