数学试题讲解

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设

D : 0 ⩽ x ⩽ 1, 0 ⩽ y ⩽ 1, sgn x = {\begin{array}{cl} 1, & x > 0, \\ 0, & x = 0, \\ - 1, & x < 0, \end{array}

则

\iint_{D} max {x, y} sgn (x - y) d x d y =