Explanation Given information: The function is g ( x , y ) = 2 + x y and vertices of triangle are ( 0 , 0 ) , ( 4 , 4 ) and ( 4 , − 4 ) . Formula used: Integral of power function is ∫ a x n d x = a [ x n + 1 n + 1 ] + C The average value z a v over R is given by, z a v = 1 A ( R ) ∫ ∫ R f ( x , y ) d y d x The area of triangle: A = 1 2 × b a s e × h e i g h t Calculation: Consider the function as: g ( x , y ) = 2 + x y Here the line segment joining the points ( 0 , 0 ) and ( 4 , 4 ) . Clearly here y = x . Also, the line joining the points ( 0 , 0 ) and ( 4 , − 4 ) . Similarly, here y = − x . Here region bounded by y = x and y = − x , and also by x = 0 and x = 4 . The area triangular region is: A ( R ) = 1 2 ⋅ 4 ⋅ 8 = 16 Also g ( x , y ) = 2 + x y Apply formula z a v = 1 A ( R ) ∫ 0 4 ∫ − x x g ( x , y ) d y d x = 1 16 ∫ 0 4 ∫ − x x ( 2 + x y ) d y d x Now evaluating inside x integral, 1 16 ∫ 0 4 ∫ − x x ( 2 + x y ) d y d x = 1 16 ∫ 0 4 ( ∫ − x x

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Chapter 6.6, Problem 38E

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To calculate: The average value of function g(x,y)=2+xy and vertices of triangle are (0,0),(4,4)

and (4,−4).

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Chapter 6.6, Problem 37E

Chapter 6.6, Problem 39E

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The average value of function g ( x , y ) = 2 + x y and vertices of triangle are ( 0 , 0 ) , ( 4 , 4 ) and ( 4 , − 4 ) .

Solution Summary: The author calculates the average value of the function g(x,y)=2+xy and the vertices of triangle are

Videos

To calculate: The average value of function g(x,y)=2+xy and vertices of triangle are (0,0),(4,4)

and (4,−4).

Want to see the full answer?

Chapter 6 Solutions

Additional Math Textbook Solutions

The average value of function g ( x , y ) = 2 + x y and vertices of triangle are ( 0 , 0 ) , ( 4 , 4 ) and ( 4 , − 4 ) .

Solution Summary: The author calculates the average value of the function g(x,y)=2+xy and the vertices of triangle are

Videos

To calculate: The average value of function g(x,y)=2+xy and vertices of triangle are (0,0),(4,4) and (4,−4).

Want to see the full answer?

Chapter 6 Solutions

Additional Math Textbook Solutions

To calculate: The average value of function g(x,y)=2+xy and vertices of triangle are (0,0),(4,4)

and (4,−4).