Assume that F(x, y, z) = e y i + xey j + (z + 1)e zk is a vector field defined on a smooth curve C given by r(t) = ti + t 2 j + t 3k for 0 ≤ t ≤ 1. Page 1 of 2 (i) Using the fundamental theorem of calculus, evaluate the line integral R C F · dr.

Assume that F(x, y, z) = e y i + xey j + (z + 1)e zk is a vector field defined on a smooth curve C given by r(t) = ti + t 2 j + t 3k for 0 ≤ t ≤ 1. Page 1 of 2 (i) Using the fundamental theorem of calculus, evaluate the line integral R C F · dr.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Assume that F(x, y, z) = e
y
i + xey
j + (z + 1)e
zk is a vector field defined on a
smooth curve C given by r(t) = ti + t
2
j + t
3k for 0 ≤ t ≤ 1.
Page 1 of 2
(i) Using the fundamental theorem of calculus, evaluate the line integral
R
C F · dr.
(ii) Show whether R
C F · dr is independent of path

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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