Final answer:
To evaluate the given double integral, we can use iterated integration. First, integrate with respect to y and then with respect to x using the given limits.
Step-by-step explanation:
To evaluate the given double integral, we can use iterated integration. Let's start by integrating with respect to y. The inner integral will have limits from 0 to 5 and the integrand will be e^(-3x + 5y).
∫05 e^(-3x + 5y) dy = e^(-3x + 5y)/5 | 05 = e^(-3x + 25) - e^(-3x).
Now we can integrate the result from the previous step with respect to x. The limits for x will be ln(3) to ln(6).
∫ln(3)ln(6) (e^(-3x + 25) - e^(-3x)) dx = [-e^(-3x + 25) + e^(-3x)] | ln(3)ln(6) = -e^(2ln(2)) + e^(ln(2)) - (e^(3ln(2)) - e^(2ln(2))).