# Power Series Representation of Improper Integral

• Jun 4th 2009, 08:24 PM
Zocken
Power Series Representation of Improper Integral
Find a power series representation for the improper integral:

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

Almost done with my difficult homework but have no clue where to start here...thanks!
• Jun 4th 2009, 10:09 PM
pickslides
$cos(t) = 1- \frac{t^2}{2!}+\frac{t^4}{4!}-\frac{t^6}{6!}+\cdots$

sub this into the integral & simplfy (Cool)