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Lemma: Riemann Integral of a Product of Continuously Differentiable Functions with Sine
Let $[a,b]$ be a closed real interval and let $f:[a,b]\to\mathbb R$ be a continuously differentiable function. For $y\in\mathbb R,$ we define the Riemann integral.
$$F(y):=\int_{a}^{b}f(x)\sin(yx)dx.$$
Then the limit of $F(y)$ tends to $0$ as $y$ tends to infinity. Formally, then $$\lim_{y\to\infty}F(y)=0.$$
Table of Contents
Proofs: 1
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983