>>13968339sorry buddy.
Youre suppose to taylor expand the cosine. This gives you a simple infinite polynomial in the integral. Then integrate the polynomial. The 0 in the lower bound means you can ignore it, and the 1 in the upper bound means x^n in the numerator doesn't matter either (1^n=1), so all u care about is the denominator for each term. The denominator in each term is like (2n+1) * (2n+2)!, so (1)*2!, (3)*4!, (5)*6!, if I did it correctly (not gonna check).
The error is at most 1/10^9, so you want to find the smallest value of n that makes the denominator bigger than 10^9. I think that's (11)*12!, so the last term should be - x^11 / (11)*12!
Again, not checking work