数学试题讲解

设

I_{1} = \iint_{D} \sin | \frac{x - y}{2} | d x d y, I_{2} = \iint_{D} \sin {(\frac{x - y}{2})}^{2} d x d y, I_{3} = \iint_{D} \sin {(\frac{x - y}{2})}^{3} d x d y

, 其中

D =

{(x, y) ∣ (x - 1)^{2} + (y - 1)^{2} ⩽ 2}

, 则

I_{1} < I_{2} < I_{3}

I_{2} < I_{3} < I_{1}

I_{3} < I_{1} < I_{2}

I_{3} < I_{2} < I_{1}