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EXAMPLE 4Using Properties of Double Integrals

If $R$ is a closed, bounded region, then

$\displaystyle\iint\limits_{\kern-3ptR} ( x^{2}y+\sin x\cos y) \,dA=\displaystyle\iint\limits_{\kern-3ptR} x^{2}y\,dA+\displaystyle\iint\limits_{\kern-3ptR}\sin x\cos y\,dA$
$\displaystyle\iint\limits_{\kern-3ptR} 8( x^{2}+y^{2})\, dA=8\displaystyle\iint\limits_{\kern-3ptR} ( x^{2}+y^{2})\, dA$