Discussion
The double integral \( \displaystyle\iint_{R} f(x,y)\,dA \) is defined as the limit of
Answer: A
The region is divided into small pieces, the function sampled in each, and \( \sum f(x_{i},y_{i})\,\Delta A_{i} \) formed; the limit as every piece shrinks is the integral. It factors into a product of single integrals only when the region is a rectangle and the integrand itself separates, which is a special case rather than the definition
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