how to integrate $\int \frac{\sin x}{x}$ in $[0,1]$

Question

I would appreciate if somebody could help me with this problem $$\int_{0}^{1}\frac{\sin{x}}{x}dx$$ here using Taylor series I got $\sum_{0}^{\infty} $$\frac{(-1)^n}{(2n+1)!(2n+1)} $ then what to do? is it the final answer ? please explain

Answer 1

You can first expand $\frac {\sin x} x$ as a Taylor series and then integrate that, or you can check out this link:

http://mathworld.wolfram.com/SineIntegral.html