ยง16.1 Line Integrals of Scalar Functions

Lecture notes

Line integrals over a curve

Masses and moments

Examples

  1. Find $\int_C \sqrt{x^2+y^2}\,ds$ when $C$ is
    1. the helix $\r(t)=2\cos(t)\i + 2\sin(t)\j + t\k,\quad 0\le t\le 4\pi;$
    2. the straight line segment from $(2,0,0)$ to $(2,0,4\pi)$.
  2. 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 $\delta(t)=\sqrt{2t^2+1}.$