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# quick integration question watch

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1. 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!!
2. but then x is a distance so a function of time?
3. 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 cannot be integrated analytically unless f(t) is a linear function of t.
4. 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)
5. does anyone have any thoughts on this?

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Updated: December 11, 2005
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