Calculate the integral of line , where and c is the circumference
How do I calculate integral of line ?
Apprentice
In English we call it a line integral
The question only makes sense If F is a vector field
Do you mean F = r = xi +yj ?
In which case use x = cos(t) y = sin(t) to parameterize the curve
r = cos(t) i +sin(t) j dr/dt = -sin(t) i +cos(t) j
On the is curve F = cos(t) i +sin(t) j
F*dr/dt = 0
Therefor the line integral is 0
If you want check out the line integral page on my website for the general method
Line Integrals
dr is understood to be the vector dx i +dy j
Recall For line integrals to actually calculate we use
integral of F(x(t),y(t)) *dr/dt as t varies from a to b
F*dr is just notation rarely used just like the notation integral(fdx+gdy)
where F = f i + g j
We use integral of F(x(t),y(t)) *dr/dt
Again check out
Line Integrals for the development of line integrals