Tension in a string (Kleppner 2.23)

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Homework Statement


A piece of string of length I and mass M is fastened into a circular loop and set spinning about the center of a circle with uniform angular velocity ω. Find the tension in the string. Suggestion: Draw a force diagram for a small piece of the loop subtending a small angle Δθ

Homework Equations



F=ma

The Attempt at a Solution



http://imgur.com/nAObr
http://imgur.com/kLLEH

No idea if its the right track, but it seemed a similar problem to one of the examples given. The answer is Mω^(2)l/4pi^(2), What I have in my integral so I think Ive done it wrong because If I integrate from 0 to 2pi(the whole string) it will cancel out one of the 2pi's
Also I have no idea what I would even use as limits for the tension.

Its from kleppners book 2.23 also btw

edit* solved it, I was off with the forces causing the circular motion. You need to take the componenets of the two tensions acting inwards and set it equal to the ma I had
 
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