Final answer:
To calculate the iterated integral of ∫∫(4xy)dydx over the region R where 0 ≤ x ≤ 3 and 0 ≤ y ≤ 1, we integrate with respect to y first and then with respect to x. The iterated integral is 4.5.
Step-by-step explanation:
To calculate the iterated integral of ∫∫(4xy)dydx over the region R where 0 ≤ x ≤ 3 and 0 ≤ y ≤ 1, we can integrate with respect to y first and then with respect to x.
First, we integrate (4xy) with respect to y from 0 to 1:
∫(4xy)dy = 2x[0.5y^2]|_0^1 = x
Next, we integrate the result with respect to x from 0 to 3:
∫x dx = (1/2)x^2|_0^3 = (1/2)(3^2) = 4.5
Therefore, the iterated integral of ∫∫(4xy)dydx over the region R is 4.5.