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**The question**

In my work [itex]\mu[/itex] is the mass per unit length, therefore I believe I can say [tex]m=\mu\Delta x[/tex]because Michael Fowler from the University of Virginia does the same at http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/AnalyzingWaves.htm (the 2nd line bellow the graph)

I start from[tex]\int^{b}_{0}\sqrt{1+\cos^{2}\left( x\right) }dx=\dfrac{\mu B}{N}[/tex] and since it is nonsensical to say [tex]\int^{b}_{0}\sqrt{1+\cos^{2}\left( x\right) }\left( dx\right)^{2}=\dfrac {mB}{N}[/tex] for a few reasons, I converted the definite integral into a Riemann sum and got [tex]\lim_{n\rightarrow\infty }\sum^{n}_{i=1}\left[\sqrt{1+\cos^{2}\left( \dfrac {b_i}{n}\right) }\right]\left( \dfrac{b}{n}\right)^{2}=\dfrac{mB}{N}[/tex]

Is this correct? Since I am dealing with [itex]\Delta x[/itex] and not [itex]dx[/itex] (which deals with infinitely small) I can bring [itex]\Delta x[/itex] to the other side from [tex]\dfrac {m B}{N\Delta x}[/tex] right? (Also [itex]\dfrac {b}{n}=\Delta x[/itex] in the Riemann sum)

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