Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, n

Question

Yuri [45]

2 years ago

15

Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, n

egative, or zero.

Mathematics

1 answer:

Harrizon [31] · Answer 1 · 2024-01-20T13:21:14+03:00

Considering the images (a),(b),(c),(d),(e),(f) the oriented path is

(a) Negative

(b) Positive

(c) Positive

(d) Zero

(e) Zero

(f) Zero

calculating each quadrant's line integral and symmetry.

In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.

What does a Line integral mean?

A line integral makes it possible to figure out a surface's area in three dimensions. Numerous situations call for the use of line integrals. They can be used, for instance, in electromagnetics to determine the work done on a charged particle moving along a curve in a force field that is represented by a vector field.

Path, curvilinear, and curve integrals are other terms for line integrals. There are several uses for line integrals, including electromagnetics, where it is used to calculate the force exerted on a charged particle moving along a curve in a force field created by a vector field.

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