# Calculating exact volume of an irregular object

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:

• This site is for Mathematica questions. – J. M.'s ennui Aug 13 '17 at 13:08
• is there a way to calculate that volume using Mathematica – Jack Aug 13 '17 at 13:14
• Yes; look up NIntegrate[]. – J. M.'s ennui Aug 13 '17 at 13:56

NIntegrate[Abs[Log[x + y]]* Boole[(x - 0.5)^2 + (y - 0.5)^2 <= 0.25],