数学题在线解答

问题:求二重积分∫∫xcosydxdy

结论/结果
1/2
解答

\begin{aligned}
& \iint_Dx\cos y \mathrm{d}x\mathrm{d}y\\
=& \int_0^1\mathrm{d}x\int_0^{\pi/2}x\cos y\mathrm{d}y\\
=& \int_0^1x\mathrm{d}x \cdot \int_0^{\pi/2}\cos y\mathrm{d}y\\
=& 1/2x^2|_0^1 \cdot \sin y|_0^{\pi/2}\\
=& 1/2 \cdot 1\\
=& 1/2
\end{aligned}

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