# Evaluate the indefinite integral as an infinite series

1. Apr 14, 2013

### KTiaam

1. The problem statement, all variables and given/known data

Evaluate the indefinite integral as an infinite series ∫ sin(x2) dx

2. Relevant equations

The Macluarin series of sin x =

Ʃ (-1)nx2n+1/(2n+1)!
n=0

The Macluarin series for sin(x2) =

Ʃ (-1)x4n+2/(2n+1)!
n=0

3. The attempt at a solution

Do i evaluate the integral of sin(x2)

from 0 to 1? then add the first couple of numbers to get a number or find a pattern?

2. Apr 14, 2013

### Dick

It's asking for an indefinite integral. The only thing you can really do is integrate the Maclaurin series term and put a summation sign in front of it.