Solve Strange Integral of (sinx)^2/x^2 from -inf to inf

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Discussion Overview

The discussion revolves around the evaluation of the integral of (sinx)^2 / (x^2) from negative infinity to infinity. Participants explore various methods for tackling this integral, including reference to known results and different mathematical techniques.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant inquires about how to approach the integral of (sinx)^2 / (x^2) from -infinity to infinity.
  • Another participant cites a table that states the answer is π.
  • Some participants suggest methods such as differentiation/integration with respect to a parameter, Laplace transforms, complex integration, and the residue theorem as potential approaches to solve the integral.
  • There is a proposal that the integral can be reduced to the integral of sin(x)/x by using integration by parts.
  • One participant expresses uncertainty about the reduction process and mentions obtaining a result of 2π using residues.
  • Another participant reiterates that the answer is π and provides a setup for integration by parts with specific choices for u and v.

Areas of Agreement / Disagreement

There is no consensus on the final value of the integral, as some participants assert it is π while at least one participant claims to have derived a different result of 2π. The discussion remains unresolved regarding the correct evaluation of the integral.

Contextual Notes

Participants reference various mathematical techniques and results, but the discussion does not clarify the assumptions or steps involved in the integration processes mentioned.

kryoo
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integral of (sinx)^2 / (x^2) from -infinity to infinity. how to tackle this
 
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I looked it up in a table. The answer is π.
 
If you want to work it out you could use differentiation/integration with respect to a parametor, laplace transforms, complex integration and the residue theorem, or it can be reduced to the integral of sin(x)/x by integration by parts.
 
lurflurf said:
If you want to work it out you could use differentiation/integration with respect to a parametor, laplace transforms, complex integration and the residue theorem, or it can be reduced to the integral of sin(x)/x by integration by parts.

so it's pi?

how do you reduce it to sinx/x with integration by parts, using resides I got 2pi
 
it is pi

u dv=u v-v du
let
u=sin(x)^2
v=-1/x
 

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