For an assignment I have to use numerical integration technique to calculate volume with cylindrical surface
Ω=(x−0.5)^2 +(y−0.5)^2 ≤0.25 and height is ln(x+y)
I have used Monte Carlo technique to calculate the volume. But to be sure the answer is correct I want to check the exact volume. I have been searching online on how to do it but couldn't find it.
So the question is, is there a way to calculate exact volume for that object or integral like this: