My Math Forum Curve integral - expression simplification

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 December 26th, 2009, 09:33 AM #1 Member   Joined: Jun 2009 Posts: 83 Thanks: 1 Curve integral - expression simplification Hi, during my computations on some curve integral I ened with this integral: $\int_{t1}^{t2}\frac{x'(t)y''(t)-y'(t)x''(t)}{(x'(t))^2+(y'(t)) ^2}dt$ Can someone please try to simplify this formula? What I think may help (but I failed) can be: polar coordinates substitution, per partes, add and subtract some expression to the nominator, nominator looks similar to the derivation of the division (x' / y')' ... Thank you for any ideas. After a while I have used substitution z = (y' / x') and got: $\int_{t1}^{t2}\frac{z'(t)}{1+(z(t))^2}dt$ but now I am still stucked.
 December 26th, 2009, 03:16 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Curve integral - expression simplification Change of variables: z' = dz/dt, so you can cancel dt and replace t1 and t2 with z(t1) and z(t2)

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