Final answer:
The integral can be recalculated by interchanging the order of integration due to the constant limits for both x and y, which simplifies to ∫_{-2}^{2}∫_{-1}^{1}(2x+3y+5)dydx, followed by integrating with respect to y first and then x.
Step-by-step explanation:
To calculate the integral of the given function by interchanging the order of integration, you start with the given double integral ∫−11∫−22(2x+3y+5)dxdy. First, we integrate with respect to x and then with respect to y, but we can also change the order of integration.
When switching the order of integration, it's important to reconsider the limits of integration for each variable, as they may change depending on the order. However, in this case, because the limits for both x and y are constants, we can directly interchange the integrals to get ∫−22∫−11(2x+3y+5)dydx.
Integrating with respect to y first, you'll find the inner integral ∫(2x+3y+5)dy, which evaluates to (2x)y + (3/2)y2 + 5y between the limits of −1 to 1. Then integrate the result with respect to x over the range from −2 to 2.
The step-by-step process would involve calculating the inner integral, plugging in the limits for y, simplifying, and then performing the outer integral with respect to x. This will give you the final answer for the double integral.