Integration over manifolds: Curve (line) integrals Calculate the curve (line) integral ∫ᶠ (1st type or tangential or work) of the 3×3 vector function (3-dimensional vector field) F(x,y,z) in 3 variables x,y,z over the curve C in the 3 dimensional xyz space
F(x,y,z)=(x+y+z,x−y,y+z)
Here: C is the (section of the) curve in the xyz space defined, parametrically, by the parameter t, by
x(t)=t+1,y(t)=t²,z(t)=t³+2
from its point A(t=0) to its point B(t=1)