Set $up$ integrals for both orders $of$ integration. Use the more convenient order $to$ evaluate the integral over the plane region $R.$

${\displaystyle \underset{R}{\overset{\phantom{}}{}}}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sinxsinydA$

$R$ : rectangle with vertices $(-,0),(,0),(,\frac{}{3}),(-,\frac{}{3})$

${\displaystyle \underset{0}{\overset{\frac{}{3}}{}}}{\displaystyle \underset{-}{\overset{\phantom{}}{}}}$

$sinxsinydxdy={\displaystyle \underset{-}{\overset{}{}}}{\displaystyle \underset{0}{\overset{\phantom{}}{}}},sinxsinydydx=$