Let A1,A2, and A3 be the regions on R2 defined by A1={(x,y):x≥0,y≥0,2x+2y−x2−y2>1>x+y},A2={(x,y):x≥0,y≥0,x+y>1>x2+y2},A3={(x,y):x≥0,y≥0,x+y>1>x3+y3}. Denote by |A1|,|A2|, and |A3| the areas of the regions A1,A2 and A3 respectively. Then

Let A1,A2, and A3 be the regions on R2 defined by A1={(x,y):x≥0,y�

1.	Let A1,A2, and A3 be the regions on R2 defined by A1={(x,y):x≥0,y≥0,2x+2y−x2−y2>1>x+y},A2={(x,y):x≥0,y≥0,x+y>1>x2+y2},A3={(x,y):x≥0,y≥0,x+y>1>x3+y3}. Denote by \|A1\|,\|A2\|, and \|A3\| the areas of the regions A1,A2 and A3 respectively. Then
Answer» Let $A_{1}, A_{2},$ and $A_{3}$ be the regions on $R^{2}$ defined by $A_{1} = {(x, y) : x \geq 0, y \geq 0, 2 x + 2 y - x^{2} - y^{2} > 1 > x + y}, A_{2} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{2} + y^{2}}, A_{3} = {(x, y) : x \geq 0, y \geq 0, x + y > 1 > x^{3} + y^{3}} .$ Denote by $\| A_{1} \|, \| A_{2} \|,$ and $\| A_{3} \|$ the areas of the regions $A_{1}, A_{2}$ and $A_{3}$ respectively. Then

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Let A1,A2, and A3 be the regions on R2 defined by A1={(x,y):x≥0,y≥0,2x+2y−x2−y2&gt;1&gt;x+y},A2={(x,y):x≥0,y≥0,x+y&gt;1&gt;x2+y2},A3={(x,y):x≥0,y≥0,x+y&gt;1&gt;x3+y3}. Denote by |A1|,|A2|, and |A3| the areas of the regions A1,A2 and A3 respectively. Then

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Let A1,A2, and A3 be the regions on R2 defined by A1={(x,y):x≥0,y≥0,2x+2y−x2−y2>1>x+y},A2={(x,y):x≥0,y≥0,x+y>1>x2+y2},A3={(x,y):x≥0,y≥0,x+y>1>x3+y3}. Denote by |A1|,|A2|, and |A3| the areas of the regions A1,A2 and A3 respectively. Then