Answer
$\int ^{1}_{0}\int ^{2y}_{y}\sin \left( x+y\right) dxdy=\sin 1\cos 1-\dfrac {\sin 3}{3}\approx 0.407$
Work Step by Step
Using computer as sled in question we get
$\int ^{1}_{0}\int ^{2y}_{y}\sin \left( x+y\right) dxdy=\sin 1\cos 1-\dfrac {\sin 3}{3}\approx 0.407$
