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quick integration question watch

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    how would you integrate

    ∫sin(ux) dt

    i assume ux is a constant as dimensions tell me so.

    would it just be tsin(ux)+c ??

    having a bit of a moment!!
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    but then x is a distance so a function of time?
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    If x is a constant then you'd just multiply it by t, as in your first post.

    If x is more complex then a simple linear function of time (ie x = at+b) then the function cannot be integrated analytically. This is evident from knowing that e^{f(t)} cannot be integrated analytically unless f(t) is a linear function of t.
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    hmm.

    i have

    x''m=-λµsin(µx)

    if when x=0 the speed is epsilon how would i go about showing the eqwn of motions is satisfied to order epsilon by

    x(t)=aEsin(ωt)

    (where E=epsilon, and a, ω are combinations of m,λ,µ)
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    does anyone have any thoughts on this?
 
 
 
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Updated: December 11, 2005

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