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From The Ramanujan Journal, 5 (2001), no. 1, 73–89.Abstract.Using Fourier transform techniques, we establish inequalities for integrals of the form $$\smallint _0^x \prod\limits_{k = 0}^n {\frac{{\sin (akx)_{} }}{{akx}}dx.} $$We then give quite striking closed form evaluations of such integrals and finish by discussing various extensions and applications.

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