Extension: Integration Using Euler's Formula

Explanations 2

• Euler's famous identity states that: eix=cos⁡x+isin⁡xe^{ix} = \cos x + i\sin xeix=cosx+isinx Replacing xxx with −x-x−x, we get: e−ix=cos⁡x−isin⁡xe^{-ix} = \cos x - i\sin xe−ix=c…

  By Sujay Kazi, Alex Federspiel

• Submitted by Sujay Kazi Define f(x)f(x)f(x) as follows: f(x)=∑n=0∞sin⁡(nx)n!.f(x) = \sum_{n=0}^{\infty}\frac{\sin(nx)}{n!}.f(x)=n=0∑∞​n!sin(nx)​. Evaluate f(π3)f\left(\frac{\pi}…

  By Alex Federspiel