The average value of f(x, y) over a region D in the plane with area A(D) is $\frac { 1 } { A ( D ) } \iint _ { D } f ( x , y ) d A$ . Find the average value of f(x, y) = xy over the region $D = \left\{ ( x , y ) \mid x ^ { 2 } + y ^ { 2 } \leq 1 , x y \geq 0 \right\}$ .

Question

Quizplus · Accepted Answer

The Answer of The average value of f(x, y) over a region D in the plane with area A(D) is $\frac { 1 } { A ( D ) } \iint _ { D } f ( x , y ) d A$ . Find the average value of f(x, y) = xy over the region $D = \left\{ ( x , y ) \mid x ^ { 2 } + y ^ { 2 } \leq 1 , x y \geq 0 \right\}$ .

The Average Value of F(x, Y) Over a Region D 1A(D)∬Df(x,y)dA\frac { 1 } { A ( D ) } \iint _ { D } f ( x , y ) d AA(D)1​∬D​f(x,y)dA

The Average Value of F(x, Y) Over a Region D $\frac { 1 } { A ( D ) } \iint _ { D } f ( x , y ) d A$