Question

Calculate the double integral ∬

R
​
xcos(2x+y)dA where R is the rectangular region 0≤x≤
6
1π
​
,0≤y≤
4
2π
​

Answer 1

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.