generalregions

Generalregions - 2D INTEGRALS FOR SIMPLE REGIONS Math21a O Knill Y-SIMPLE REGIONS A class of regions is what is bound between the graphs of two

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Unformatted text preview: 2D INTEGRALS FOR SIMPLE REGIONS Math21a, O. Knill Y-SIMPLE REGIONS. A class of regions is what is bound between the graphs of two functions c ( x ) and d ( x ). Such regions are sometimes called y-simple regions . One can write the region as R = { ( x, y ) | c ( x ) ≤ y ≤ d ( x ) } . An integral over such a region is an iterated integral which is: integraltextintegraltext R f dA = integraltext b a integraltext d ( x ) c ( x ) f ( x, y ) dydx X-SIMPLE REGIONS. It is defined by two functions a ( y ) and b ( y ) which are functions of y . One can write the region as R = { ( x, y ) | a ( y ) ≤ x ≤ b ( y ) } . An integral over such a region is an iterated integral: integraltextintegraltext R f dA = integraltext d c integraltext b ( y ) a ( y ) f ( x, y ) dxdy EXAMPLE 1) Integrate f ( x, y ) = x 2 over the region bounded above by sin( x 3 ) and bounded below by the grapy of- sin( x 3 ) for 0 ≤ x ≤ π . The value of this integral has a physical meaning....
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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