# Line integral?

bfr
If a question says something like: "evaluate $$\int$$(x*z*y)dx - (x-y)dy + (x^3)dz from (1,0,0,) to (1,0,2pi) along the curve (x,y,z)=(cos(t),sin(t),t)" or something like that, this is just basically splitting up a line integral? In my example, it would be the same as: $$\int$$cos(t)*t*sin(t)) * (-sin(t)) dt - $$\int$$(cos(t)-sin(t))*cos(t) dt ... etc. , which is just: $$\int$$<(cos(t)*t*y),-(cos(t)-y),(cos(t)^3)> dot <-sin(t),cos(t),1> dt from t=0 to t=1 ("dot" represents a dot product).

Unco
If a question says something like: "evaluate $$\int$$(x*z*y)dx - (x-y)dy + (x^3)dz from (1,0,0,) to (1,0,2pi) along the curve (x,y,z)=(cos(t),sin(t),t)" or something like that, this is just basically splitting up a line integral? In my example, it would be the same as: $$\int$$cos(t)*t*sin(t)) * (-sin(t)) dt - $$\int$$(cos(t)-sin(t))*cos(t) dt ... etc. , which is just: $$\int$$<(cos(t)*t*y),-(cos(t)-y),(cos(t)^3)> dot <-sin(t),cos(t),1> dt from t=0 to t=1 ("dot" represents a dot product).
Pretty much, though the limits would be from t=0 to t=2pi, and it's the second form of the integral (i.e. the expanded dot product) that is useful to calculate (by evaluating the definite integral with respect to t).

bfr
OK, thanks.

And, er, yeah, I meant from t=0 to t=2pi.