Explanation Given info: f ( x , y , z ) = e z W: x + y + z ≤ 1 , x ≥ 0 , y ≥ 0 Concept used: First draw the plane x + y + z = 1 Identify the region such that W: x + y = z = 1 , x ≥ 0 , y ≥ 0 Take projection of this on x y plane element show Form this decide the limit of x and y 0 ≤ y ≤ 1 − x 0 ≤ x ≤ 1 ∫ ∫ E ∫ f ( x , y , z ) d v = ∫ D ∫ [ ∫ u 1 ( x , y ) u 2 ( x , y ) f ( x , y , z ) d z ] d A u 1 ( x , y ) = 0 u 2 ( x , y ) : z ≤ 1 − x − y To decide take projection on x y plane x ≥ 0 , y ≥ 0 , x + y = 1 , y = 1 − x = ∫ 0 1 ∫ 0 1 − x [ ∫ 0 1 − x − y e z d z ] d y d x ( r e w r i t e the expression and integrate w .r .t z ) = ∫ 0 1 ∫ 0 1 − x ( e 1 − x − y − 1 ) d y d x Integrate w.r...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Chapter 16.3, Problem 13E

To determine

Evaluate $\int \int_{W} \int f (x, y, z) dv$ for the function $F$ and region $W$ specified. $f (x, y, z) {= e}^{2}, W: x + y + z \leq 1, x \geq 0, y \geq 0$

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Chapter 16.3, Problem 12E

Chapter 16.3, Problem 14E

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Evaluate ∫ ∫ W ∫ f ( x , y , z ) dv for the function F and region W specified. f ( x , y , z ) = e 2 , W: x + y + z ≤ 1 , x ≥ 0 , y ≥ 0

Solution Summary: The author explains how to determine the dv for the function F and the specified region.

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Evaluate $\int \int_{W} \int f (x, y, z) dv$ for the function $F$ and region $W$ specified. $f (x, y, z) {= e}^{2}, W: x + y + z \leq 1, x \geq 0, y \geq 0$

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Chapter 16 Solutions

Evaluate ∫ ∫ W ∫ f ( x , y , z ) dv for the function F and region W specified. f ( x , y , z ) = e 2 , W: x + y + z ≤ 1 , x ≥ 0 , y ≥ 0

Solution Summary: The author explains how to determine the dv for the function F and the specified region.

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Evaluate ∫∫W∫f(x,y,z) dv for the function Fand region W specified.f(x,y,z)= e2, W: x+y+z≤1, x≥0, y≥0

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Chapter 16 Solutions

Evaluate $\int \int_{W} \int f (x, y, z) dv$ for the function $F$ and region $W$ specified. $f (x, y, z) {= e}^{2}, W: x + y + z \leq 1, x \geq 0, y \geq 0$