HLTA02H3 Lecture 8: Lecture 8

For each of the following vector fields FF, decide whether it is conservative or not by computing curl FF. Type in a potential function ff (that is, ∇f=F∇f=F). Assume the potential function has a value of zero at the origin. If the vector field is not conservative, type N.

F(x,y,z)=6xi+7yj+k
f(x,y,z)=f(x,y,z)=

equation editor

Equation Editor

D. F(x,y)=(6siny)i+(−6y+6xcosy)j
f(x,y)=

F(x,y)=(4xy3+8)i+(6x2y2+2e2y)jF(x,y)=(4xy3+8)i+(6x2y2+2e2y)j

is conservative by finding a potential function ff for FF, and use ff to compute ∫CF⋠dr∫CF⋠dr, where CC is the curve given by

r(t)=2sin9ti+2tπsin105tjr(t)=2sin9⁡ti+2tπsin10⁡5tj

for 0≤t≤π/20≤t≤π/2.