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Math Help - Taylor Series integraton

  1. #1
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    Taylor Series integraton

    f(x) = [integral from 0 to x] tan−1(t)dt based at b = 0.
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  2. #2
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    \frac{1}{1+t^2} = \frac{1}{1 - (-t^2)} = 1 - t^2 + t^4 - t^6 + ...

    integrate term for term ...

    \arctan{t} = C + t - \frac{t^3}{3} + \frac{t^5}{5} - \frac{t^7}{7} + ...

    since \arctan(0) = 0 ... C = 0

    \arctan{t} = t - \frac{t^3}{3} + \frac{t^5}{5} - \frac{t^7}{7} + ...

    o.k. ... integrate \arctan{t}
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  3. #3
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    ok

    so when there's a problem stating arctan, I immediately change it to 1/(1+x^2)?
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  4. #4
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    you're speaking in absolutes, and no one can tell you to always do it this way.

    suffice it to say that it's one nice method to find the power series for the arctan function
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