- #1

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I am reading a paper in which the following integral is presented

$$\int_{-\infty}^{ct-x} \int_{-\infty}^{ct-x} J (2t - \frac{2x+s_1+s_2}{c}) \frac{\mathrm{d}f (s_1)}{\mathrm{d}s_1} \frac{\mathrm{d}f(s_2)}{\mathrm{d}s_2} \mathrm{d}s_1 \mathrm{d}s_2$$

where J and f are unknwon functions.

Now, it seems that for "sufficiently large c the integration can be carried out to yield"

$$\int_{-\infty}^{ct-x} \int_{-\infty}^{ct-x} J (2t - \frac{2x}{c})\big \lbrack f(s_1) \vert^{ct-x}_{-\infty} f(s_2) \vert^{ct-x}_{-\infty} \big \rbrack$$

but I can not follow, why would the term $$\frac{2x}{c}$$ "survive" the limiting process as c goes to infinity?

Many thanks as usual