This post categorized under Vector and posted on August 12th, 2019.

The line integral of a vector field plays a crucial role in vector calculus. Out of the four fundamental theorems of vector calculus three of them involve line integrals of vector fields. Greens theorem and Stokes theorem relate line integrals around closed curves to double integrals or surface integrals .Properties of Line Integrals of Vector Fields. The line integral of vector function has the following properties Let (C) denote the curve (AB) which is traversed from (A) to (B) and let (-C) denote the curve (BA) with the opposite orientation from (B) to (A.) Tgraphiche line integral of a vector field can be derived in a manner very similar to the case of a scalar field but this time with the inclusion of a dot product. Again using the above definitions of F C and its parametrization r(t) we construct the integral from a Riemann sum.

VECTOR INTEGRATION LINE INTEGRALS SURFACE INTEGRALS VOLUME INTEGRALS. Integration of vector functions. In ordinary calculus we compute integrals of real functions of a real variable that is we compute integrals of functions of the type y f(x) where x and y are real numbers.

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