+5 What is the solution to this? I've never seen this notation before.
Same with me, I've not seen this notation before, so this could be wrong.
I think that the e's are unit vectors and that we are being given the parametric equations of the line of integration.
\(x=u^{2},\quad y=2u, \quad z=u^3\)
from which
\(2xyz^{2}=2.u^{2}.2u.(u^{3})^{2}=4u^{9},\)
and
\(dr=e_{x}dx+e_{y}dy+e_{z}dz=e_{x}2u\, du+e_{y}2\, du+e_{z}3u^{2} du\)
So,
\(\displaystyle \int_{L}2xyz^{2}\, dr=e_{x}\int^{1}_{0}4u^{9}.2u\,du+e_{y}\int^{1}_{0}4u^{9}.2\, du+e_{z}\int^{1}_{0}4u^{9}.3u^{2}\,du \\ =(8/11)e_{x}+(4/5)e_{y}+e_{z}.\)
Apologies if that's a load of rubbish !
