Double_integrals_9-10_through_12

Double_integrals_9-10_through_12 - Double Integrals and...

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1 Double Integrals and Green’s Theorem ± This unit is based on Sections 9.10 through 9.12 , 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 double integrals in Cartesian and polar Use double integrals to evaluate area, volume, center of mass, moment of inertia,…etc. use Green’s theorem to convert a line integral along a boundary of a into a double integral, and to convert a double integral to a line integral along the boundary of a region use Green’s theorem to evaluate line integrals, and to determine work, area and moment of inertia. ± Reading : Read Section 9.10 - 9.12, pages 505-524. ± Exercises : Complete problems
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2 ± The integral over the region R may be calculated by 2 successive integrations: ∫∫ R dxdy y x f ) , ( 2. Similarly, for integrating first over x and then over y ∫∫ ∫ ∫ = R b a x g x g dx dy y x f dxdy y x f ) ( ) ( 2 1 ) , ( ) , ( ± Double integrals may be written in the form ∫∫ ∫ ∫ = R d c y h y h dy dx y x f dxdy y x f ) ( ) ( 2 1 ) , ( ) , ( 1. We may integrate first over y, keeping x constant with proper limits of integration and then the whole expression is integrated w.r.t. x Double integrals in Cartesian coord.
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3 Engineering Application of double integrals ±
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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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Double_integrals_9-10_through_12 - Double Integrals and...

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