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I'm trying to calculate the following function (at x=1) with accuracy of 10^(-3).

[tex]f(x)= \int^x_{0} \frac{1-cost}{t}[/tex]

What I've tried:

[tex]f(1)=f(0)+f'(c)=1-\sum_{k=0}^\infty \frac{(-1)^nc^{2k}}{(2k)!}[/tex]

But now I don't know how to calculate this expression. [I know that this series is convergent thanks to Leibniz criterion]

Have I done something wrong?

[tex]f(x)= \int^x_{0} \frac{1-cost}{t}[/tex]

What I've tried:

[tex]f(1)=f(0)+f'(c)=1-\sum_{k=0}^\infty \frac{(-1)^nc^{2k}}{(2k)!}[/tex]

But now I don't know how to calculate this expression. [I know that this series is convergent thanks to Leibniz criterion]

Have I done something wrong?

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