The Cauchy Schwartz inequality for integrals on a bounded domain reads \begin{align} \int_{-a}^{a} f^2(x) dx \geq \frac{1}{2a}\left(\int_{-a}^a f(x) dx \right)^2 \end{align} Can the difference be expressed using only $\int_{-a}^a f(x)dx$ terms? If not is such an approximation possible?
2026-03-28 22:36:59.1774737419
What is missing to make integral Cauchy Schwartz inequality an equality
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