# Thread: solving integral problem by complex analysis method

1. ## solving integral problem by complex analysis method

I got this problem to solve but have no much confidence in my solution. Can anyone help me. Thanks in advance.

Anyone?

3. ## Re: solving integral problem by complex analysis method

Originally Posted by firebird
Anyone?
Always there is someone. You have correctly found $\displaystyle CPV=\lim_{R\to +\infty}\int_{-R}^Rf(x)\;dx$ (Cauchy Principal Value). As the given integral is convergent then, $\displaystyle \int_{-\infty}^{+\infty}f(x)\;dx=CPV=\pi/\sqrt{2}$

4. ## Re: solving integral problem by complex analysis method

Originally Posted by FernandoRevilla
Always there is someone. You have correctly found $\displaystyle CPV=\lim_{R\to +\infty}\int_{-R}^Rf(x)\;dx$ (Cauchy Principal Value). As the given integral is convergent then, $\displaystyle \int_{-\infty}^{+\infty}f(x)\;dx=CPV=\pi/\sqrt{2}$
Thank you very much.

5. ## Re: solving integral problem by complex analysis method

Originally Posted by firebird
Thank you very much.
You are welcome.