Evaluate the indefinite integral as an infinite series

[KTiaam]

Homework Statement

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

Homework 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

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?

 

[Dick]

Homework Statement

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

Homework 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

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?

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.