Explanation Given info: ∫ 0 1 ∫ 3 4 ∫ 6 7 f ( x , y , z ) d z d y d x Concept used: ∫ r s ∫ c d ∫ a b f ( x , y , z ) d x d y d z In the above expression integrate first with respect to x (keeping y and z fixed), then integrate with respect toy ( keeping z fixed ) and finally integrate with respect to z . There are five other possible orders in which we can integrate all of which give the same value. But you have to care about limit, order of integration should be same as order of limit, otherwise gives different result and variable should decreased continuously during integration. Ex: ∫ r s ∫ c d ∫ a b f ( x , y , z ) d x d y d z = ∫ r s ∫ a b ∫ c d f ( x , y , z ) d y d x d z ≠ ∫ r s ∫ c d ∫ a b f ( x , y , z ) d x d z

3rd Edition

ISBN: 9781464114885

Author: Jon Rogawski, Colin Adams

Publisher: W. H. Freeman

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Question

Chapter 15.3, Problem 1PQ

To determine

Which of $(a) - (c)$ is note equal to $\int_{0}^{1} \int_{3}^{4} \int_{6}^{7}$ $f (x, y, z) d z d y d x$ ?

(a) $\int_{6}^{7} \int_{0}^{1} \int_{3}^{4} f (x, y, z) d y d x d z$

(p) $\int_{3}^{4} \int_{0}^{1} \int_{6}^{7} f (x, y, z) d z d x d y$

(ee) $\int_{0}^{1} \int_{3}^{4} \int_{6}^{7} f (x, y, z) d z d z d y$

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Chapter 15.2, Problem 68E

Chapter 15.3, Problem 2PQ

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Chapter 15 Solutions

Calculus: Early Transcendentals

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Knowledge Booster

Which of ( a ) − ( c ) is note equal to ∫ 0 1 ∫ 3 4 ∫ 6 7 f ( x , y , z ) d z d y d x ? (a) ∫ 6 7 ∫ 0 1 ∫ 3 4 f ( x , y , z ) d y d x d z (p) ∫ 3 4 ∫ 0 1 ∫ 6 7 f ( x , y , z ) d z d x d y (ee) ∫ 0 1 ∫ 3 4 ∫ 6 7 f ( x , y , z ) d z d z d y

Which of (a)−(c)is note equal to ∫01∫34∫67f(x,y,z)dzdydx? (a) ∫67∫01∫34f(x,y,z)dydxdz (p) ∫34∫01∫67f(x,y,z)dzdxdy (ee)∫01∫34∫67f(x,y,z)dzdzdy

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Chapter 15 Solutions