∫∫_[D] cos(x + y) dxdy
= ∫[0→π] dy ∫[0→y] cos(x + y) dx
= ∫[0→π] {sin(x + y) |[0→y]} dy
= ∫[0→π] {sin(y + y) - sin(0 + y)} dy
= ∫[0→π] (sin2y - siny) dy
= {(- 1/2)cos2y + cosy} |[0→π]
= {cos(π) - (1/2)cos(2π)} - {cos(0) - (1/2)cos(0)}
= - 2
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