Explanation Find the vector field and its differential and integrate the dot product Given : f ( x , y , z ) = x 2 + y 2 + z 2 Formula used : Calculation : The vectors are r ( t ) = ( c o s t , s i n t , t ) f o r 0 ≤ t ≤ π Therefore, r ' ( t ) = 〈 − sin t , cos t , 1 〉 ‖ r ' ( t ) ‖ = sin 2 t + ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 17.2, Problem 5E

To determine

To Calculate:

The integral of the scalar function or vector field over $r (t) = (c o s t, s i n t, t) f o r 0 \leq t \leq π$

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Chapter 17.2, Problem 4E

Chapter 17.2, Problem 6E

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Chapter 17 Solutions

Calculus - Standalone book

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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The integral of the scalar function or vector field over r ( t ) = ( c o s t , s i n t , t ) f o r 0 ≤ t ≤ π

Solution Summary: The author calculates the integral of the scalar function or vector field over r ( t ) = (c o

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To Calculate:

The integral of the scalar function or vector field over $r (t) = (c o s t, s i n t, t) f o r 0 \leq t \leq π$

Want to see the full answer?

Chapter 17 Solutions

The integral of the scalar function or vector field over r ( t ) = ( c o s t , s i n t , t ) f o r 0 ≤ t ≤ π

Solution Summary: The author calculates the integral of the scalar function or vector field over r ( t ) = (c o

Concept explainers

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To Calculate: The integral of the scalar function or vector field over r(t) = (cost,sint,t) for 0≤t≤π

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Chapter 17 Solutions

To Calculate:

The integral of the scalar function or vector field over $r (t) = (c o s t, s i n t, t) f o r 0 \leq t \leq π$