So I have to use the type I type II region formula to find the volume under the equation (2x-y) and over the circular domain with center (0,0) and radius 2. Do I have to split this circle into semi-circles and treat it as 2 type I domains? I got the following limits for the top half, but I get stuck when integrating:
The Attempt at a Solution
Upper: Sqrt(2 - x^2) from the equation 2 = y^2 + x^2
So I have to find the integral with respect to y of 2x-y with limits 0 to Sqrt[2-x^2]
After integrating with respect to Y I got:
2x(Sqrt[2-x^2]) - 1 + (x^2)/2
Is this correct to start with? Then integrate with respect to x from -2 to 2?