Line Integral

2 Given r(u) = x(u)e1 + y(u)e2 + z(u)e3 where r(u) is a position vector defining a curve c connecting point Pi to P2 where u = u1 and u = u2 respectively, anf given A(x, y, z) = A1 e1 + A2e2 + A3e3 being a vectorial function defined and continuous along c, then the integral of the tangential component of A along c from P1 to P2 is given by

J P1 Jc JC

If A were a force, then this integral would represent the corresponding work.

3 If the contour is closed, then we define the contour integral as


/ A-dr is independent of the path c connecting P1 to P2 (5.5-a)

0 0

Post a comment