Find a power series representation for the improper integral:

$\displaystyle \int^{x}_{0}\frac{1-cost}{t^2}dt$

Almost done with my difficult homework but have no clue where to start here...thanks!

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- Jun 4th 2009, 07:24 PMZockenPower Series Representation of Improper Integral
Find a power series representation for the improper integral:

$\displaystyle \int^{x}_{0}\frac{1-cost}{t^2}dt$

Almost done with my difficult homework but have no clue where to start here...thanks! - Jun 4th 2009, 09:09 PMpickslides
$\displaystyle cos(t) = 1- \frac{t^2}{2!}+\frac{t^4}{4!}-\frac{t^6}{6!}+\cdots$

sub this into the integral & simplfy (Cool)