Which of the following statements are true for all vector fields, and which are true only for conservative vector fields? (a) The line integral along a path from P to Q does not depend on which path is chosen. (b) The line integral over an oriented curve C does not depend on how C is parametrized. (c) The line integral around a closed curve is zero. (d) The line integral changes sign if the orientation is reversed. (e ) The line integral is equal to the difference of a potential function at the two endpoints. (f) The line integral is equal to the integral of the tangential component along the curve. (g) The cross partial derivatives of the components are equal. 3
Which of the following statements are true for all vector fields, and which are true only for conservative vector fields? (a) The line integral along a path from P to Q does not depend on which path is chosen. (b) The line integral over an oriented curve C does not depend on how C is parametrized. (c) The line integral around a closed curve is zero. (d) The line integral changes sign if the orientation is reversed. (e ) The line integral is equal to the difference of a potential function at the two endpoints. (f) The line integral is equal to the integral of the tangential component along the curve. (g) The cross partial derivatives of the components are equal. 3
Which of the following statements are true for all vector fields, and which are true only for conservative vector fields? (a) The line integral along a path from P to Q does not depend on which path is chosen. (b) The line integral over an oriented curve C does not depend on how C is parametrized. (c) The line integral around a closed curve is zero. (d) The line integral changes sign if the orientation is reversed. (e ) The line integral is equal to the difference of a potential function at the two endpoints. (f) The line integral is equal to the integral of the tangential component along the curve. (g) The cross partial derivatives of the components are equal. 3
Which of the following statements are true for all vector fields, and which are true only for conservative vector fields? (a) The line integral along a path from P to Q does not depend on which path is chosen. (b) The line integral over an oriented curve C does not depend on how C is parametrized. (c) The line integral around a closed curve is zero. (d) The line integral changes sign if the orientation is reversed. (e ) The line integral is equal to the difference of a potential function at the two endpoints. (f) The line integral is equal to the integral of the tangential component along the curve. (g) The cross partial derivatives of the components are equal. 3
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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