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=== Two dimensions === In two dimensions, the domain <math>A</math> may be divided into a number of two-dimensional cells <math>A_i</math> such that <math display="inline">A = \bigcup_i A_i</math>. Each cell then can be interpreted as having an "area" denoted by <math>\Delta A_i</math>.<ref>{{cite book |last1=Ostebee |first1=Arnold |last2=Zorn |first2=Paul |year=2002 |title=Calculus from Graphical, Numerical, and Symbolic Points of View |edition=Second |page=M-34 |quote=We chop the plane region ''R'' into ''m'' smaller regions ''R''<sub>1</sub>, ''R''<sub>2</sub>, ''R''<sub>3</sub>, ..., ''R''<sub>''m''</sub>, perhaps of different sizes and shapes. The 'size' of a subregion ''R''<sub>''i''</sub> is now taken to be its ''area'', denoted by Ξ''A''<sub>''i''</sub>.}}</ref> The two-dimensional Riemann sum is <math display="block">S = \sum_{i = 1}^n f(x_i^*, y_i^*)\, \Delta A_i,</math> where <math>(x_i^*, y_i^*) \in A_i</math>.
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