(Solved): Given the power series representation \( \cos x=\sum \frac{(-1)^{n} x^{2 n}}{(2 n) !} \), find a po ...

Given the power series representation \( \cos x=\sum \frac{(-1)^{n} x^{2 n}}{(2 n) !} \), find a power series representation for \( \int \cos \left(x^{2}\right) d x \) and use the first 4 terms of the series to approximate the definite integral on the interval \( [0,1] \)