Explanation Given info: f ( x , y , z ) = x y z ; W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ 1 − x 2 , 0 ≤ x ≤ 1 Concept used: Limit of y is a function of x , so first integrate w.r.t to y . Then either w.r.t to x or z Calculation: d v = d x d y d x ∭ w f ( x , y , z ) . d x f ( x , y , z ) = x y z w: 0 ≤ z ≤ 1, 0 ≤ y ≤ 1 − x 2 , 0 ≤ x ≤ 1 = ∫ 0 1 ∫ 0 1 ∫ 0 1 − x 2 x y z d y d x d z ( putting the value of function ) (Integrate w.r.t to y then put limit, assuming z and x as constant) = ∫ 0 1 ∫ 0 1 z x ∫ 0 1 − x 2 ( y d y ) d x d z ( rewrite the expression ) ( use ∫ y d y = y 2 2 ) = ∫ 0 1 ∫ 0 1

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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Question

Chapter 16.3, Problem 11E

To determine

Evaluate $\underset{w}{∭} f (x, y, z) dv$ for the function f and region specified. $f (x, y, z) = x y z; W: 0 \leq z \leq 1, 0 \leq y \leq \sqrt{1 - x^{2}}, 0 \leq x \leq 1$

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Chapter 16.3, Problem 10E

Chapter 16.3, Problem 12E

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Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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Evaluate ∭ w f ( x , y , z ) dv for the function f and region specified. f ( x , y , z ) = x y z ; W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ 1 − x 2 , 0 ≤ x ≤ 1

Solution Summary: The author evaluates w f ( x, y ) dv for the function and region specified.

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Evaluate $\underset{w}{∭} f (x, y, z) dv$ for the function f and region specified. $f (x, y, z) = x y z; W: 0 \leq z \leq 1, 0 \leq y \leq \sqrt{1 - x^{2}}, 0 \leq x \leq 1$

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Chapter 16 Solutions

Evaluate ∭ w f ( x , y , z ) dv for the function f and region specified. f ( x , y , z ) = x y z ; W: 0 ≤ z ≤ 1 , 0 ≤ y ≤ 1 − x 2 , 0 ≤ x ≤ 1

Solution Summary: The author evaluates w f ( x, y ) dv for the function and region specified.

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Evaluate ∭wf(x,y,z) dv for the function f and region specified.f(x,y,z)= xyz ; W: 0≤z≤1, 0≤y≤1−x2, 0≤x≤1

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Chapter 16 Solutions

Evaluate $\underset{w}{∭} f (x, y, z) dv$ for the function f and region specified. $f (x, y, z) = x y z; W: 0 \leq z \leq 1, 0 \leq y \leq \sqrt{1 - x^{2}}, 0 \leq x \leq 1$