Final answer:
The double integral of functions u and v over an area in the first quadrant is generally represented as ∫∫(u * v) dA. The actual computation would require specific limits of integration for the given area.
Step-by-step explanation:
To find the double integral of functions u and v in the first quadrant, you need to set up the integral in terms of area. A double integral allows you to add up a function over a two-dimensional area, and the notation usually involves dA, representing an infinitesimal element of area. Depending on the specific problem, you may need to integrate the product, sum, or difference of the two functions. However, the letter choices provided (A to D) simply show different operations between the two functions; they do not specify integration over the first quadrant or any particular bounds. To properly integrate over the first quadrant, you would need to include the limits of integration for both variables that define this quadrant. If you're given two functions u and v and you're asked to find the double integral of the product of these functions, which will accumulate the results over some area, the correct form would be:
A) ∫∫(u * v) dA
Remember that the actual limits of integration would need to be specified for it to be computable for a particular area in the first quadrant.