Explanation Given info: ( a ) ∫ 0 1 ∫ 0 x ∫ 0 x 2 + y 2 f ( x , y , z ) d z d y d x ( b ) ∫ 0 1 ∫ 0 1 − x 2 ∫ 2 4 f ( x , y , z ) d z d y d x Concept used: ∭ E f ( x , y , z ) d x d y d z = ∫ a b ∫ g 1 ( x ) g 2 ( x ) ∫ u 1 ( x , y ) u 2 ( x , y ) f ( x , y , z ) d z d y d x E = { ( x , y , z ) | a ≤ x ≤ b , g 1 ( x ) ≤ y ≤ g 2 ( x ) , u 1 ( x , y ) ≤ z ≤ u 2 ( x , y ) | } Projection of E on x y plane is W = { ( x , y ) | a ≤ x ≤ b , g 1 ( x ) ≤ y ≤ g 2 ( x ) | } Calculation: ∫ 0 1 ∫ 0 x ∫ 0 x 2 + y 2 f ( x , y , z ) d z d y d x = ∫ ∫ E ∫ f ( x , y , z ) d z d y dx E = { ( x , y , z ) | 1 ≤ x ≤ 0 , 0

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 16.3, Problem 3PQ

To determine

Describe the projection of the region of integration $W$ onto the $x y -$ plane.

(a) $\int_{0}^{1} \int_{0}^{x} \int_{0}^{x^{2} + y^{2}} f (x, y, z) d z d y d x$

(q) $\int_{0}^{1} \int_{0}^{\sqrt{1 - x^{2}}} \int_{2}^{4} f (x, y, z) d z d y d x$

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Chapter 16.3, Problem 2PQ

Chapter 16.3, Problem 1E

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Chapter 16 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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Describe the projection of the region of integration W onto the x y − plane. (a) ∫ 0 1 ∫ 0 x ∫ 0 x 2 + y 2 f ( x , y , z ) d z d y d x (q) ∫ 0 1 ∫ 0 1 − x 2 ∫ 2 4 f ( x , y , z ) d z d y d x

Solution Summary: The author explains the projection of the region of integration W onto the x y plane.

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Describe the projection of the region of integration $W$ onto the $x y -$ plane.

(a) $\int_{0}^{1} \int_{0}^{x} \int_{0}^{x^{2} + y^{2}} f (x, y, z) d z d y d x$

(q) $\int_{0}^{1} \int_{0}^{\sqrt{1 - x^{2}}} \int_{2}^{4} f (x, y, z) d z d y d x$

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Chapter 16 Solutions

Describe the projection of the region of integration W onto the x y − plane. (a) ∫ 0 1 ∫ 0 x ∫ 0 x 2 + y 2 f ( x , y , z ) d z d y d x (q) ∫ 0 1 ∫ 0 1 − x 2 ∫ 2 4 f ( x , y , z ) d z d y d x

Solution Summary: The author explains the projection of the region of integration W onto the x y plane.

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Describe the projection of the region of integration W onto the xy−plane. (a) ∫01∫0x∫0x2+y2 f(x,y,z)dz dy dx (q) ∫01∫01−x2∫24 f(x,y,z)dz dy dx

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Chapter 16 Solutions

Describe the projection of the region of integration $W$ onto the $x y -$ plane.

(a) $\int_{0}^{1} \int_{0}^{x} \int_{0}^{x^{2} + y^{2}} f (x, y, z) d z d y d x$

(q) $\int_{0}^{1} \int_{0}^{\sqrt{1 - x^{2}}} \int_{2}^{4} f (x, y, z) d z d y d x$