Let $a,b,p$ be any positive real numbers with $a\geq b.$ Then it appears that $f(x)=\int_0^{2\pi}|a+e^{i\theta}bx|^pd\theta$ is an increasing function on $(0,1).$ May I know how to establish this?
2026-04-11 23:53:18.1775951598
Integral as an increasing function
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