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If f(x, y) > 0 for all points (x, y) in R, then can be interpreted geometrically as... The area of region R SSR f(x, y)dA The volume of the solid obtained by revolving region R around the x-axis The volume of the solid obtained by revolving region R around the y-axis The volume of the solid that lies above R and below f's graph.

If f(x, y) > 0 for all points (x, y) in R, then can be interpreted geometrically as... The area of region R SSR f(x, y)dA The volume of the solid obtained by revolving region R around the x-axis The volume of the solid obtained by revolving region R around the y-axis The volume of the solid that lies above R and below f's graph.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
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If \( f \) is some function of two variables, and \( R \) is the region depicted below, **Graph Explanation:** - The graph shows a coordinate plane with \( x \)-axis and \( y \)-axis. - There is a closed, irregularly shaped region marked as \( R \) on the plane. - The region \( R \) is enclosed within a boundary that curves and loops around. - The axes have arrows indicating the positive directions of \( x \) (to the right) and \( y \) (upward). This region \( R \) could represent the domain of integration or area over which the function \( f(x, y) \) is evaluated.
Transcribed Image Text:If \( f \) is some function of two variables, and \( R \) is the region depicted below, **Graph Explanation:** - The graph shows a coordinate plane with \( x \)-axis and \( y \)-axis. - There is a closed, irregularly shaped region marked as \( R \) on the plane. - The region \( R \) is enclosed within a boundary that curves and loops around. - The axes have arrows indicating the positive directions of \( x \) (to the right) and \( y \) (upward). This region \( R \) could represent the domain of integration or area over which the function \( f(x, y) \) is evaluated.
If \( f(x, y) > 0 \) for all points \((x, y)\) in \( R \), then \[ \iint_R f(x, y) \, dA \] can be interpreted geometrically as... - ○ The area of region R - ○ The volume of the solid obtained by revolving region R around the x-axis - ○ The volume of the solid obtained by revolving region R around the y-axis - ○ The volume of the solid that lies above R and below \( f \)'s graph.
Transcribed Image Text:If \( f(x, y) > 0 \) for all points \((x, y)\) in \( R \), then \[ \iint_R f(x, y) \, dA \] can be interpreted geometrically as... - ○ The area of region R - ○ The volume of the solid obtained by revolving region R around the x-axis - ○ The volume of the solid obtained by revolving region R around the y-axis - ○ The volume of the solid that lies above R and below \( f \)'s graph.
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