Show the work for all 6 problems please

1. Find the integral [ dy [ dx ( er ) =? Hint: the antiderivative fedx does not exist. 2. Find the Volume of the body in the upper-half-space ( z 2 0 ) that is outside of the cylinder x3 + yz = 4 and inside the sphere x3 + y2 + z =16. 3. Find the integral [ dy dx [ dz (xz) = ? Vi- ( x - + x ] ) 4. Find the integral [ dx ] dy ] dz (z) =? 5. Determine whether the Vector Field F(x, y) = > is conservative, and if it is find the potential f (x, y) such that F = Vf . 6. Determine whether the Vector Field F(x, y) = is conservative, and integrate it along the positively oriented triangle with vertices P,(0, 0) , P2 (2, 0), P, (2, 6)