Explanation Given: a. f ( x , y , z ) = y b. x 2 + y 2 + z 2 ≤ 1 c. x , y , z ≤ 0 Formula Used: Spherical coordinates of a point Q ( x , y , z ) are defined by ρ , ϕ , θ where, • ρ is the length of the radius vector to the point Q . • φ is the angle between the projection of the radius vector O Q → on the -plane x y and the x - axis; • θ Is the angle of deviation of the radius vector O Q → from the positive direction of the z -axis (Figure 1). Spherical coordinates of a point are related to its Cartesian coordinates as: x = ρ c o s φ s i n θ , y = ρ s i n φ s i n θ , z = ρ c o s θ And d x d y d z = ρ 2 s i n θ d ρ d φ d θ Where, ρ ≥ 0 , 0 ≤ φ ≤ 2 π , 0 ≤ θ ≤ π Calculation: Part (a.) ∭ R y d x d y d z R is the region of integration. Converting the triple integral to spherical coordinates by putting, x = ρ c o s φ s i n θ , y = ρ s i n φ s i n θ , z = ρ c o s θ And x , y , z ≤ 0 x 2 + y 2 + z 2 ≤ 1 New limits are, ρ ≤ 1 , 0 ≤ φ ≤ π 2 , 0 ≤ θ ≤ π 2 ∭ R y d x d y d z ∭ R ( ρ s i n φ s i n θ ) ρ 2 s i n θ d ρ d φ d θ ∭ R ...

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Chapter 16.4, Problem 45E

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Triple integration of $f (x, y, z)$ .

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Chapter 16.4, Problem 44E

Chapter 16.4, Problem 46E

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Chapter 16 Solutions

EBK CALCULUS

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Prob. 26CRE Ch. 16 - Prob. 27CRE Ch. 16 - Prob. 28CRE Ch. 16 - Prob. 29CRE Ch. 16 - Prob. 30CRE Ch. 16 - Prob. 31CRE Ch. 16 - Prob. 32CRE Ch. 16 - Prob. 33CRE Ch. 16 - Prob. 34CRE Ch. 16 - Prob. 35CRE Ch. 16 - Prob. 36CRE Ch. 16 - Prob. 37CRE Ch. 16 - Prob. 38CRE Ch. 16 - Prob. 39CRE Ch. 16 - Prob. 40CRE Ch. 16 - Prob. 41CRE Ch. 16 - Prob. 42CRE Ch. 16 - Prob. 43CRE Ch. 16 - Prob. 44CRE Ch. 16 - Prob. 45CRE Ch. 16 - Prob. 46CRE Ch. 16 - Prob. 47CRE Ch. 16 - Prob. 48CRE Ch. 16 - Prob. 49CRE Ch. 16 - Prob. 50CRE Ch. 16 - Prob. 51CRE Ch. 16 - Prob. 52CRE Ch. 16 - Prob. 53CRE Ch. 16 - Prob. 54CRE Ch. 16 - Prob. 55CRE Ch. 16 - Prob. 56CRE Ch. 16 - Prob. 57CRE Ch. 16 - Prob. 58CRE Ch. 16 - Prob. 59CRE Ch. 16 - Prob. 60CRE Ch. 16 - Prob. 61CRE

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Triple integration of f ( x , y , z ) .

Solution Summary: The author explains how to determine the triple integration of f (x, y, and z) by converting a triple integral to spherical coordinates.

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Triple integration of $f (x, y, z)$ .

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Chapter 16 Solutions

Triple integration of f ( x , y , z ) .

Solution Summary: The author explains how to determine the triple integration of f (x, y, and z) by converting a triple integral to spherical coordinates.

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Triple integration of f(x,y,z).

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Chapter 16 Solutions

Triple integration of $f (x, y, z)$ .