Final answer:
To calculate the double integral ∬ R xcos(2x+y)dA, use the given limits to perform the integration.
Step-by-step explanation:
To calculate the double integral ∬ R xcos(2x+y)dA, where R is the rectangular region 0≤x≤2π and 0≤y≤4π, we need to integrate the function over the given region.
Starting with the outer integral, which is the integral with respect to x, we use the limits 0 and 2π. Then, for the inner integral, we integrate with respect to y, using the limits 0 and 4π.
Therefore, the double integral becomes ∫02π ∫04π xcos(2x+y) dy dx.