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mymathcourses Group Title

Suppose C is any curve from( 0,0,0) to (1,1,1) and F(x,y,z)=(5z+5y)i+(2z+5x)j+(2y+5x)k . Compute the line integral ∫Fdr .

  • one year ago
  • one year ago

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  1. him1618 Group Title
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    dr = dxi + dyj + dzk

    • one year ago
  2. mymathcourses Group Title
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    could explain more clearly? @him1618

    • one year ago
  3. him1618 Group Title
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    you know dr, and you know F..can u tell me the expression for F.dr?

    • one year ago
  4. experimentX Group Title
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    it might depend on your path ... what path do you choose to take?

    • one year ago
  5. henpen Group Title
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    It doesn't depend on the path as the curl=0

    • one year ago
  6. experimentX Group Title
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    then you can choose any path. easiest one ... choose a straight line parametric form of line is r(t) = (0,0,0) + t(1,1,1) ... change all x,y,z in F into this parametric form. i.e. = t,t,t ... integrate it wrt dt ... from 0 to 1

    • one year ago
  7. mymathcourses Group Title
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    @experimentX but it is said for any curve, thats why i dont know how to solve this problem, not a straight line or sth else, just for any?

    • one year ago
  8. experimentX Group Title
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    as henpen said earlier, take a curl, if the curl is zero, then the line integral does not depend on path. choose any path.

    • one year ago
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