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In Problems 31-34, find the average value of each function over the given rectangle. 31. f(x, y) = (x + y)²; R = {(x, y) |1 ≤ x ≤ 5, -1 ≤ y ≤ 1} 32. f(x, y) = x² + y²; = {(x, y) | -1 ≤ x ≤ 2, 1 ≤ y ≤ 4} 33. f(x, y) = x/y; R = 34. f(x, y) = x²y³; R = In Problems 35 20 {(x, y) |1 ≤ x ≤ 4, 2 ≤ y ≤7} {(x,y) | -1 ≤ x ≤ 1, 0≤ y ≤ 2} please help with 31,33,35, and 37

In Problems 31-34, find the average value of each function over the given rectangle. 31. $f(x,y)=(x+y)_{2}R={(x,y)∣1≤x≤5,−1≤y≤1} $ 32. $f(x,y)=x_{2}+y_{2}R={(x,y)∣−1≤x≤2,1≤y≤4} $ 33. $f(x,y)=x/y;R={(x,y)∣1≤x≤4,2≤y≤7}$ 34. $f(x,y)=x_{2}y_{3};R={(x,y)∣−1≤x≤1,0≤y≤2}$
In Problems 31-34, find the average value of each function over the given rectangle. 31. $f(x,y)=(x+y)_{2}R={(x,y)∣1≤x≤5,−1≤y≤1} $ 32. $f(x,y)=x_{2}+y_{2};R={(x,y)∣−1≤x≤2,1≤y≤4} $ 33. $f(x,y)=x/y;R={(x,y)∣1≤x≤4,2≤y≤7}$ 34. $f(x,y)=x_{2}y_{3};R={(x,y)∣−1≤x≤1,0≤y≤2}$ In Problems 35-38, find the volume of the solid under the graph of each function over the given rectangle. 35. $f(x,y)=2−x_{2}−y_{2}$; $R={(x,y)∣0≤x≤1,0≤y≤1}$ 36. $f(x,y)=5−x;R={(x,y)∣0≤x≤5,0≤y≤5}$ 37. $f(x,y)=4−y_{2};R={(x,y)∣0≤x≤2,0≤y≤2}$ 38. $f(x,y)=e_{−x−y};R={(x,y)∣0≤x≤1,0≤y≤1}$

In this solution we find the average value of the function

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