[list=1][*]Divide the region into a tringle and a circular sector as shown. [/*][*]Compute [math]\alpha[/math] by using an arc-trig function in the triangle. [/*][*]Compute [math]\beta[/math] as a complement of [math]\alpha[/math]. [/*][*]Compute the double integral on the pink region using polar transformation. [/*][*]Use double integral in xy for the green region noting that one of the bounds of the inner integral is non-constant. [/*][*] Add the result of the two integrals.[/*][/list]