Discussion
For a rectangular region with constant limits and an integrand \( f(x)g(y) \), the double integral
Answer: C
When the limits do not depend on the other variable and the integrand factorises, the inner integral of \( g \) is a constant that passes out of the outer one:
\[ \iint f(x)g(y)\,dA \;=\; \left(\int f(x)\,dx\right)\left(\int g(y)\,dy\right). \]
Both conditions are needed: a variable limit or a non-separable integrand destroys the factorisation
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