Integrate[
      Integrate[10 - 2 x - y, {x, y - 4, 5 - y/2}], {y, 0, 6}]

Integrate[
        Integrate[Exp[-x^2 - y^2], {x, 0, (Sqrt[8 - y^2])}], {y, 2, 
          2 (Sqrt[ 2])}] + 
      Integrate[
        Integrate[Exp[-x^2 - y^2], {x, 0, y}], {y, 0, 2}]

NIntegrate[
        Integrate[Exp[-x^2 - y^2], {x, 0, (Sqrt[8 - y^2])}], {y, 2, 
          2 (Sqrt[ 2])}] + 
      Integrate[
        Integrate[Exp[-x^2 - y^2], {x, 0, y}], {y, 0, 2}]

Integrate[
      Integrate[Exp[-r^2] r, {r, 0, 2 (Sqrt[ 2])}], {th, Pi/4, 
        Pi/2}]

NIntegrate[
      Integrate[Exp[-r^2] r, {r, 0, 2 (Sqrt[ 2])}], {th, Pi/4, 
        Pi/2}]