SOLUTION: Evaluate the line integral ∫F⋅dr where F=⟨−3sin(x),−3cos(y),xz⟩ and C is the path given by r(t)=(2t^3,3t^2,−3t) for 0≤t≤1 ∫F⋅dr=

Algebra ->  Equations -> SOLUTION: Evaluate the line integral ∫F⋅dr where F=⟨−3sin(x),−3cos(y),xz⟩ and C is the path given by r(t)=(2t^3,3t^2,−3t) for 0≤t≤1 ∫F⋅dr=      Log On


   



Question 1181931: Evaluate the line integral ∫F⋅dr where F=⟨−3sin(x),−3cos(y),xz⟩ and C is the path given by r(t)=(2t^3,3t^2,−3t) for 0≤t≤1
∫F⋅dr=

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+2t%5E3, y+=+3t%5E2, and z+=+-3t
r%28t%29+=+%28matrix%281%2C3%2C+2t%5E3%2C+3t%5E2%2C+-3t%29%29 ==> dr%28t%29+=+%28matrix%281%2C3%2C6t%5E2%2C6t%2C-3%29%29dt

==>
= int%28-18t%5E2sin%282t%5E3%29-18tcos%283t%5E2%29%2B18t%5E4%2C+dt%2C0%2C1%29
=
=
=
=3cos2-3sin3+%2B+3%2F5