Solution Found!
Calculate the line integral of the function from the
Chapter 1, Problem 29P(choose chapter or problem)
Calculate the line integral of the function from the origin to the point (1,1,1) by three different routes:
(a) (0, 0, 0) → (1, 0, 0) → (1, 1, 0) → (1, 1, 1).
(b) (0, 0, 0) → (0, 0, 1) → (0, 1, 1) → (1, 1, 1).
(c) The direct straight line.
(d) What is the line integral around the closed loop that goes out along path (a) and back along path (b)?
Questions & Answers
QUESTION:
Calculate the line integral of the function from the origin to the point (1,1,1) by three different routes:
(a) (0, 0, 0) → (1, 0, 0) → (1, 1, 0) → (1, 1, 1).
(b) (0, 0, 0) → (0, 0, 1) → (0, 1, 1) → (1, 1, 1).
(c) The direct straight line.
(d) What is the line integral around the closed loop that goes out along path (a) and back along path (b)?
ANSWER:Part (a)
Step 1 of 10
A line integral is integral that is taken along a curve. The function is continuously varying along the curve. We are going to find the line integral of the given function.
The function is
The infinitesimal displacement vector
The path consists of 3 parts they are
(i) from (0, 0, 0) to (1, 0, 0)
,
,
,
Since the y and z components do not vary, the line integral of those components is zero.
Therefore the function is modified as
The displacement vector is expressed as
The line integral
