Explanation Given info: f ( x , y , z ) = x + y W: y ≤ z ≤ x , 0 ≤ y ≤ x , 0 ≤ x ≤ 1 Concept used: First perform integration w.r.t z because limit of z is function of x and y . Then perform integration w.r.t y . Because limit of y is only function x . At last perform integration w.r.t x, because limit of x is constant. Calculation: ∭ w f ( x ) dv dv = d x d y dz in any order = ∭ w ( x + y ) d z d y d x ( putting the value of function and dv ) W: y ≤ z ≤ x , 0 ≤ y ≤ x , 0 ≤ x ≤ 1 Put the limit in same order ∫ 0 1 ∫ 0 x ∫ y x ( x + y ) d z d y d x ( first integrate with respect to z assuming x , y as constant ) (Integrate with respect to y treat x as consta...

4th Edition

ISBN: 9781319323394

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 9E

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

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Chapter 16.3, Problem 8E

Chapter 16.3, Problem 10E

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Chapter 16 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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

Solution Summary: The author explains how to determine the value of function and region.

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

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

Solution Summary: The author explains how to determine the value of function and region.

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Evaluate ∫∫W∫f(x,y,z) dv for the function and region Wspecified f(x,y,z)=x+y, W: y≤z≤x, 0≤y≤x, 0≤x≤1

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Chapter 16 Solutions

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