ยง16.1 Line Integrals of Scalar Functions
Lecture notesLine integrals over a curve
Masses and moments
Examples
-
Find $\int_C \sqrt{x^2+y^2}\,ds$ when $C$ is
- the helix $\r(t)=2\cos(t)\i + 2\sin(t)\j + t\k,\quad 0\le t\le 4\pi;$
- the straight line segment from $(2,0,0)$ to $(2,0,4\pi)$.
-
Find the center of mass of a wire lying along the curve
\[ \r(t) = t\i + t^2\j + (1-t)\k,\quad 0\le t\le 1\]
with density $\delta(t)=\sqrt{2t^2+1}.$