Section 15.3: Integration in Polar Coordinates

Use polar coordinates to combine the sum \[ \int_{1/\sqrt{2}}^1 \int_{\sqrt{1-x^2}}^x xy dy dx + \int_1^{\sqrt{2}} \int_0^x xy dy dx + \int_{\sqrt{2}}^2 \int_0^{\sqrt{4-x^2}} xy dy dx \] into one double integral. Then evaluate the double integral.