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Kira J

Post Number: 7
Posted on Sunday, 01 May, 2011 - 11:19 am:   

x=a*exp(bu)cos(u), y=a*exp(bu)sin(u)

wish to integrate [x'(u)*y"(u)-y'(u)x"(u)]/(x'(u)2+y'(u)2) with respect to u. Looks like the form of the integrand has something to do with the quotient rule but I don't know what. I think the question is certainly not intended so that I will have to find out what the derivatives are and the integrate.

Can anyone help?
Daniel Fretwell
Veteran poster

Post Number: 1280
Posted on Sunday, 01 May, 2011 - 11:55 am:   

This looks like something related to (but isnt) curvature.

The denominator would have to be to the power 3/2 for this to be true.

However, if you plod through the workings you will find a nice surprise at the end. Things will simplify nicely.
Simon Taylor
Veteran poster

Post Number: 449
Posted on Sunday, 01 May, 2011 - 12:13 pm:   

There is an outrageous bit of 'look it looks like this', but it is almost impossible to find unless you have seen it before. It isn't using quotient rule. Solving the hard way is tedious but works.
Veteran poster

Post Number: 2143
Posted on Sunday, 01 May, 2011 - 12:35 pm:   

What you want to integrate is a nice function in terms of h(u):=y'(u)/x'(u) and h'(u), can you see that?

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