I don't see why you would need a pi in the equation since you're not doing a circle.

Perhaps you can integrate by parts, your first integration limits for your x is 0 to 2, y limits: 3x to 6, your second integration limit would probably be; x limit: 0 to 2, y limit: 6 to (the top curve equation)... But i don't see why you can't just integrate the whole thing in on equation.. x limit: 0 to 2, y limit: 3x to (curve equation).... If I'm wrong somebody please correct me...