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Other

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Integration over the region in the plane between the graphs of two continuous functions is performed by setting up type I or type II domains in Cartesian coordinates or as a polar domain in polar coordinates. Double integrals require a student to visualize the differential element of area covering the desired domain of integration. Using an integrand function of value 1 everywhere generates a double integral whose value is the area of the domain. A plane region ... is type I if it lies between the graphs of two continuous functions ... and ... of ... on [ ... , ... ], that is, ... . Vertical strips ... are integrated as ... shown by "x strip history" control. A plane region ... is type II if it lies between the graphs of two continuous functions ... and ... of ... on [ ... , ... ], that is, ... . Horizontal strips ... are integrated as ... shown by "y strip history" control. When the domain consists of two type II domains as shown in the plot, a transition occurs from one domain to the other where the integral over the first domain is added to the integral over the second domain. ... , where ... , ... , and ... are continuous on [ ... , ... ]. For a polar wedge the domain is defined by ... , where ... and ... are continuous on ... . Radial strips ... are integrated as ... shown by "wedge history" control.

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      EUN,LOM,LRE4,work-cmr-id:262452,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/DifferentialElementDA/,ilox,learning resource exchange,LRE metadata application profile,LRE

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