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Chapter15.pdf
Preview of University of California
🔗 Source: math.ucdavis.edu
📊 Size: 2.39 MB
📄 Pages: 24 pages
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Summary

The volume beneath a surface over a rectangular region is given by a double integral, which can be evaluated using iterated integrals. Reversing the order of integration gives the same answer. The double integral of a function f(x, y) over a region R is denoted as ∫∫_R f(x, y) dA. To evaluate this integral, the region R is partitioned into small rectangular cells, and the function is integrated over each cell. The limit of the sum of these integrals as the partition is refined is the double integral. The double integral can be evaluated using iterated integrals, with the order of integration either dy dx or dx dy. The properties of double integrals include linearity, commutativity, associativity, and distributivity. Examples of evaluating double integrals over rectangular and non-rectangular regions are given, including finding the volume of a solid bounded by a surface and a region in the xy-plane.

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Description

The volume beneath a surface over a rectangular region is given by a double integral, which can be evaluated using iterated integrals.

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  • File Format: PDF
  • File Size: 2.39 MB
  • Pages: 24
  • Language: EN
  • Total Downloads: 287
  • Last Updated: 1 week ago

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