Let be the integrals:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{-\infty}^{\infty}dx Cos(uf(x)) [/tex] (or the same but a sine) and

[tex] \int_{-\infty}^{\infty}dxe^{-ag(x)} [/tex]

Where "a" is a a>0 positive constant, u can be either positive or negative.. and g(x)>0 for every real x.. my question is will these integrals "always2 exist under these conditions?..what would happen if we take the limit a-->oo and u-->oo ? are in this case equal to 0?

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# Existence of integrals:

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