Explanation Definition used: Volume of the surface: If f ( x , y ) ≥ 0 over the rectangle R = { ( x , y ) | a ≤ x ≤ b , c ≤ y ≤ d } , then the volume of the solid formed by graphing f over the rectangle R is given by V = ∬ R f ( x , y ) d A . Calculation: Given that the region is R = { ( x , y ) | 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 } . Compute the integral with respect to y . ∫ 0 1 ∫ 0 1 e − x − y d y d x = ∫ 0 1 [ ∫ 0 1 e − x − y d y ] d x = ∫ 0 1 [ [ − e − x − y ] 0 1 ] d x Apply the limit value for y . ∫ 0 5 ∫ 0 5 5 − x d y d x = ∫ 0 1 [ [ − e − x − 1 + e − x ] ] d x Compute the integral with respect to x

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Chapter 7.6, Problem 38E

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To find: The volume of the solid under the graph of the function f(x,y)=e−x−y over the given rectangle.

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Chapter 7.6, Problem 37E

Chapter 7.6, Problem 39E

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Chapter 7 Solutions

EP CALCULUS F/BUS.,ECON.-BRIEF-ACCESS

Ch. 7.1 - Prob. 1MP Ch. 7.1 - Matched Problem 2 Find f(2, 2, 3) for f in Example...Ch. 7.1 - Prob. 3MP Ch. 7.1 - Matched Problem 4 For the box in Example 4, find...Ch. 7.1 - Matched Problem 5 Refer to Example 5. Find the...Ch. 7.1 - Matched Problem 6 Find the coordinates of the...Ch. 7.1 - Matched Problem 7 (A) Describe the cross sections...Ch. 7.1 - Explore and Discuss 1 Imagine that you are facing...Ch. 7.1 - In Problems 18, find the indicated value of the...Ch. 7.1 - Prob. 2E

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The volume of the solid under the graph of the function f ( x , y ) = e − x − y over the given rectangle.

Solution Summary: The author calculates the volume of the solid formed by graphing f over the rectangle R by calculating the integral with respect to y.

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To find: The volume of the solid under the graph of the function f(x,y)=e−x−y over the given rectangle.

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Chapter 7 Solutions