Explanation Substitute the given values of r(t) in the given function and obtain the value of f ( r ( t ) ) and d s Given : Let f ( x , y , z ) = x + y z and let C be the line segment from P = ( 0 , 0 , 0 ) to ( 6 , 2 , 2 ) Formula used : d s = ‖ r ' ( t ) ‖ d t Calculation : We substitute x = 6 t , y = 2 t , z = To determine (b) To Calculate : Evaluate ∫ C f ( x , y , z ) d s

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on …

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Chapter 17.2, Problem 1E

To determine

(a)

To Calculate:

Calculate $f (r (t))$ and $d s = ‖ r' (t) ‖ d t$ for the parametrization $r (t) = (6 t, 2 t, 2 t), 0 \leq t \leq 1$

To determine

(b)

To Calculate:

Evaluate $\int_{C} f (x, y, z) d s$

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Chapter 17.2, Problem 4PQ

Chapter 17.2, Problem 2E

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Chapter 17 Solutions

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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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(a) To Calculate : Calculate f ( r ( t ) ) and d s = ‖ r ' ( t ) ‖ d t for the parametrization r ( t ) = ( 6 t , 2 t , 2 t ) , 0 ≤ t ≤ 1

Solution Summary: The author explains how to calculate f ( r ) and d s using the previous solution.

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(a)

To Calculate:

Calculate $f (r (t))$ and $d s = ‖ r' (t) ‖ d t$ for the parametrization $r (t) = (6 t, 2 t, 2 t), 0 \leq t \leq 1$

(b)

To Calculate:

Evaluate $\int_{C} f (x, y, z) d s$

Want to see the full answer?

Chapter 17 Solutions

(a) To Calculate : Calculate f ( r ( t ) ) and d s = ‖ r ' ( t ) ‖ d t for the parametrization r ( t ) = ( 6 t , 2 t , 2 t ) , 0 ≤ t ≤ 1

Solution Summary: The author explains how to calculate f ( r ) and d s using the previous solution.

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(a) To Calculate: Calculate f(r(t)) and ds =‖r'(t)‖dt for the parametrization r(t)=(6t,2t,2t),0≤t≤1

(b) To Calculate: Evaluate ∫Cf(x,y,z)ds

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Chapter 17 Solutions

(a)

To Calculate:

Calculate $f (r (t))$ and $d s = ‖ r' (t) ‖ d t$ for the parametrization $r (t) = (6 t, 2 t, 2 t), 0 \leq t \leq 1$

(b)

To Calculate:

Evaluate $\int_{C} f (x, y, z) d s$