MathDB
Integrable Function

Source: BdMO 2023 Higher Secondary National P5

February 12, 2023
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Problem Statement

Consider an integrable function f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} such that af(a)+bf(b)=0af(a)+bf(b)=0 when ab=1ab=1. Find the value of the following integration: ∫0∞f(x) dx \int_{0}^{\infty} f(x) \,dx
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