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 ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.4, Problem 45E

To determine

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

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

Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.1 - Prob. 45E Ch. 16.1 - Prob. 46E Ch. 16.1 - Prob. 47E Ch. 16.1 - Prob. 48E Ch. 16.1 - Prob. 49E Ch. 16.1 - Prob. 50E Ch. 16.1 - Prob. 51E Ch. 16.1 - Prob. 52E Ch. 16.1 - 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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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