Check the box next to each statement if it must be true. If a vector field F is tangent to a curve C at every point of C, then the flux integral of F across C is 0. If all points of a solid region in R³ satisfy x > 0, then the center of mass (x, y, z) of that region also satisfies > 0. If the parameterization of C is reversed, swapping start and end, the value of the scalar line integral f f(x, y, z) ds changes sign. Jo F. dr is 0 for every closed curve C, then F is conservative. In spherical coordinates, the equation = c, where c is a constant, specifies a plane or half-plane. If the vector line integral
Check the box next to each statement if it must be true. If a vector field F is tangent to a curve C at every point of C, then the flux integral of F across C is 0. If all points of a solid region in R³ satisfy x > 0, then the center of mass (x, y, z) of that region also satisfies > 0. If the parameterization of C is reversed, swapping start and end, the value of the scalar line integral f f(x, y, z) ds changes sign. Jo F. dr is 0 for every closed curve C, then F is conservative. In spherical coordinates, the equation = c, where c is a constant, specifies a plane or half-plane. If the vector line integral
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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Transcribed Image Text:Check the box next to each statement if it must be true.
If a vector field F is tangent to a curve C at every point of C, then the flux integral of F
across C is 0.
If all points of a solid region in R³ satisfy x ≥ 0, then the center of mass (x, y, z) of that
region also satisfies x > 0.
If the parameterization of C is reversed, swapping start and end, the value of the scalar line
integral f(x, y, z) ds changes sign.
If the vector line integral
F. dr is 0 for every closed curve C, then F is conservative.
C
In spherical coordinates, the equation = c, where c is a constant, specifies a plane or
half-plane.
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