Sign funtion

Calculus Level 5

Define \(\displaystyle f(x)=\frac{x}{2}[1+sgn(x)]\)

Then , \(\displaystyle \int\limits_{-\infty}^{\infty} e^{-2\lambda\pi ix}f(x)dx = \frac{i\delta'(\lambda)}{a\pi^b} - \frac{c}{d\pi^f \lambda^g}\)

\(\textbf{Evaluate}\)

\( a+b+c+d+f+g\)

\(\textbf{Details and Assumptions}\)

  1. \(sgn(x)=\frac{|x|}{x}\) is the sign or signum function.

  2. \(\lambda \in\) R.

  3. \(\delta(x)\) is the delta function.

  4. \(i=\sqrt{-1}\)

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