Explanation Given information: ∫ 0 2 t 0 r ( t ) d t , ∫ t 0 2 t 0 r ( t ) d t , ∫ 2 t 0 3 t 0 r ( t ) d t Concept used: Rank from least to greatest means rank in increasing order. Calculation: If F ' ( t ) is continuous for a ≤ t ≤ b , then ∫ a b F ' ( t ) d t = F ( b ) − F ( a ) . Let ∫ r ( t ) d t = F ( t ) and t 0 = 1 The values of integrals are ∫ 2 t 0 3 t 0 r ( t ) d t = ∫ 2 3 r ( t ) d t = [ F ( t ) ] 2 3 = F ( 3 ) − F ( 2 ) It represents quantity of oil pumped out during the period t = 2 to t = 3 . ∫ t 0 2 t 0 r ( t ) d t = ∫ 1 2 r ( t ) d t = [ F ( t ) ] 1 2 = F ( 2 ) − F ( 1 ) It represents quantity of oil pumped out during the period t = 1 and t = 2 . ∫ 0 2 t 0 r ( t ) d t = ∫ 0 2 r ( t ) d t = [ F ( t ) ] 0 2 = F ( 2 ) − F ( 0 ) It represents quantity of oil pumped out during the period t = 0 to t = 2

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 5.5, Problem 19P

To determine

Rank in order from least to greatest.

∫02t0r(t)dt, ∫t02t0r(t)dt, ∫2t03t0r(t)dt

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Chapter 5.5, Problem 18P

Chapter 5.5, Problem 20P

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(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

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Chapter 5 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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Rank in order from least to greatest. ∫ 0 2 t 0 r ( t ) d t , ∫ t 0 2 t 0 r ( t ) d t , ∫ 2 t 0 3 t 0 r ( t ) d t

Solution Summary: The author explains how Rank from least to greatest means rank in increasing order.

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Rank in order from least to greatest.

∫02t0r(t)dt, ∫t02t0r(t)dt, ∫2t03t0r(t)dt

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Chapter 5 Solutions

Rank in order from least to greatest. ∫ 0 2 t 0 r ( t ) d t , ∫ t 0 2 t 0 r ( t ) d t , ∫ 2 t 0 3 t 0 r ( t ) d t

Solution Summary: The author explains how Rank from least to greatest means rank in increasing order.

Concept explainers

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Rank in order from least to greatest. ∫02t0r(t)dt, ∫t02t0r(t)dt, ∫2t03t0r(t)dt

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Chapter 5 Solutions

Rank in order from least to greatest.

∫02t0r(t)dt, ∫t02t0r(t)dt, ∫2t03t0r(t)dt