# Fresnel integrals

#### Fernando Revilla

##### Well-known member
MHB Math Helper
I quote a unsolved question posted in MHF by user poorbutttryagin on February 5th, 2013.

I read 'functions of one complex variable by Conway'

186pg, 7.7. Prove that int_0^inf sin(t^2) dt = sqrt(pi/8)

What is the starting point?

Any comment or hint is welcomed !

Thanks !

#### Fernando Revilla

##### Well-known member
MHB Math Helper
Have a look at the pdf here:

120. Integrales de Fresnel | Fernando Revilla

P.S. 1 Although it is in Spanish, I think that one can follow the outline looking only at the formulas.

P.S. 2 There is a typo in the second line of the pdf.:

It should be $I_2=\displaystyle\int_0^{+\infty}\sin x^2\;dx$ instead of $I_2=\displaystyle\int_0^{+\infty}\cos x^2\;dx$

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#### ZaidAlyafey

##### Well-known member
MHB Math Helper
I see that you are using contour integration to solve the integral .

Do you have another method to solve it ?

#### Fernando Revilla

##### Well-known member
MHB Math Helper
Do you have another method to solve it ?
I know another metod (Laplace transform), but it is not in my site. Have a look (for example) here:

Fresnel Integrals.