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mymathcourses

  • 3 years ago

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 .

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  1. him1618
    • 3 years ago
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    dr = dxi + dyj + dzk

  2. mymathcourses
    • 3 years ago
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    could explain more clearly? @him1618

  3. him1618
    • 3 years ago
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    you know dr, and you know F..can u tell me the expression for F.dr?

  4. experimentX
    • 3 years ago
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    it might depend on your path ... what path do you choose to take?

  5. henpen
    • 3 years ago
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    It doesn't depend on the path as the curl=0

  6. experimentX
    • 3 years ago
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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

  7. mymathcourses
    • 3 years ago
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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?

  8. experimentX
    • 3 years ago
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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.

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