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

[kryoo]

integral of (sinx)^2 / (x^2) from -infinity to infinity. how to tackle this

 

[mathman]

I looked it up in a table. The answer is π.

 

[lurflurf]

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.

 

[kryoo]

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

 

[lurflurf]

it is pi

u dv=u v-v du
let
u=sin(x)^2
v=-1/x