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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## 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.

Ask a homework question - tutors are online