Recent content by iFargle

  1. I

    Series representation of a function

    So then that would be... C+x^{2}\sum^{\infty}_{n=0}(-1)^{n}\frac{x^{6n+3}}{2n+1}=C+\sum^{\infty}_{n=0}(-1)^{n}\frac{x^{6n+5}}{2n+1} or am I missing something huge? I don't get what you mean by evaluate the integration constant.
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    Series representation of a function

    \int\frac{1}{1-(-x^2)}dx=\int\sum(-x^{2})^{n}dx =\sum(-1)^{n}\frac{x^{2n+1}}{2n+1}dx Correct? I still feel like my answer is wrong, though.
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    Series representation of a function

    Sorry, it was supposed to read: tan^{-1}(x)=\int\frac{1}{x^2+1}dx Got carried away with formatting, haha
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    Series representation of a function

    I think I have it. I am overjoyed! Tell me if this is correct: f(x)=x^2tan^{-1}(x^3) First, \frac{d}{dx}tan^{-1}(x) = \frac{1}{x^2+1} \int(tan^{-1}(x))dx=\int\frac{1}{x^2+1}dx Rearranging it so it resembles the geometric series: \int\frac{1}{1-(-x^2)}dx=\int\sum((-x^2)^n)dx Integrated...
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    Series representation of a function

    Homework Statement Find a power series representation for the function and determine the radius of convergence.Homework Equations f(x)=x^{2}tan^{-1}(x^{3})The Attempt at a Solution I don't have any idea on how to even start this. First I differentiated \frac{d}{dx} arctan(x)=\frac{1}{x^2+1}...
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    Maple [Maple 14] rightbox in a procedure?

    Bump?
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    Maple [Maple 14] rightbox in a procedure?

    Here's what I have >Integral:=proc(f,i) local JExact,S,R,E; JExact:=int(f,x=0..1); S:=rightsum(f,x=0..1,i); R:=evalf(%); E:=evalf(abs(JExact-R)); RETURN( [Integral]=JExact, [Right_Sum]=S, [Right_Sum_Eval]=R, [Error]=E ); end; Integral...