3. Let ki dx + k2 dy + k3 dz be a constant 1-form and let a, b, and č be any three points in a, y, z space. Prove that the integral of this 1-form from a to c is the sum of the integral from ã to b plus the integral from b to c. 4. Using the result of Exercise 3, prove that the amount of work done by a constant force field in moving a particle from a to b along a path composed of straight line segments is independent of the path.
3. Let ki dx + k2 dy + k3 dz be a constant 1-form and let a, b, and č be any three points in a, y, z space. Prove that the integral of this 1-form from a to c is the sum of the integral from ã to b plus the integral from b to c. 4. Using the result of Exercise 3, prove that the amount of work done by a constant force field in moving a particle from a to b along a path composed of straight line segments is independent of the path.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![3. Let ki dx + k2 dy + k3 dz be a constant 1-form and let a, b, and č be
any three points in a, y, z space. Prove that the integral of this 1-form
from a to c is the sum of the integral from ã to b plus the integral
from b to c.
4. Using the result of Exercise 3, prove that the amount of work done
by a constant force field in moving a particle from a to b along a path
composed of straight line segments is independent of the path.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2Fd5fcfbd2-3d6e-4a0e-a1ae-aeb1ef05cb81%2Fm6pga2t.png&w=3840&q=75)
Transcribed Image Text:3. Let ki dx + k2 dy + k3 dz be a constant 1-form and let a, b, and č be
any three points in a, y, z space. Prove that the integral of this 1-form
from a to c is the sum of the integral from ã to b plus the integral
from b to c.
4. Using the result of Exercise 3, prove that the amount of work done
by a constant force field in moving a particle from a to b along a path
composed of straight line segments is independent of the path.
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