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Line integral: Quiz

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Question 1: This answer can be also verified by the ________.
Residue theoremCauchy's integral formulaCauchy's integral theoremCauchy–Riemann equations

Question 2: The "________" of quantum mechanics actually refers not to path integrals in this sense but to functional integrals, that is, integrals over a space of paths, of a function of a possible path.
Quantum electrodynamicsQuantum field theoryPath integral formulationPropagator

Question 3: The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly ________ or, for a vector field, the scalar product of the vector field with a differential vector in the curve).
CalculusArc lengthDerivativePi

Question 4:
Which of the following titles did Line integral have?
Exponential Integral
Topological Methods in the Theory of Nonlinear Integral Equations
Integral Equations
Path integral

Question 5: For a vector field F : URnRn, the line integral along a piecewise smooth ________ CU, in the direction of r, is defined as
Elliptic curveManifoldCurveAlgebraic geometry

Question 6: If a vector field F is the ________ of a scalar field G, that is,
GradientDivergenceDerivativeCurl (mathematics)

Question 7: A line integral of a scalar field is thus a line integral of a vector field where the vectors are always ________ to the line.
DerivativeManifoldTangentTrigonometric functions

Question 8: Due to the ________ the curl of the vector field corresponding to the conjugate of a holomorphic function is zero.
Conformal mapCauchy's integral formulaDerivativeCauchy–Riemann equations

Question 9: Integral
Lists of integrals
________
Integration by:
parts, disks, cylindrical
shells
, substitution,
trigonometric substitution,
partial fractions, changing order
Continuous functionImproper integralDerivativeImplicit and explicit functions

Question 10: The function to be integrated may be a scalar field or a ________.
Vector calculusGradientVector fieldCurl (mathematics)







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