$f(x),g(x):[0,1]\to [0,1]$,Prove that:$$\int_0^1f(g(x))dx\leqslant \int_0^1f(x)dx+\int_0^1g(x)dx$$ The solution uses $F(x)=f(x)-x$ and turns the problem into:$$\int_0^1F(g(x))dx\leqslant \frac12$$ Is there more obvious or essential approach?
2026-04-28 20:54:57.1777409697
Is there a more essential solution to this problem?
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