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Let $f,g : \mathbb{R} \to \mathbb{R}$. Is it acceptable to write $\int_a^b fg$ instead of $\int_a^b f(x)g(x)\,dx$ (i.e., would it throw others off while reading it)? The (lack of an) indeterminate is unambiguous since the function $fg$ only accepts one argument, but I've never seen others write it like that.

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    I believe you can handle it. Was observing from grading too many calculus final exams that there is significant correlation between leaving out $dx$ and getting the wrong answer for $\int \frac{dx}{1+3x}$.2012-11-27

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I wouldn't do that, a) because it looks ugly to me, and, perhaps more importantly, b) because it prevents you from writing things like

$ \int_0^{\pi}fg\sin\theta\,\mathrm d\theta=\int_{-1}^1fg\,\mathrm d\cos\theta\;. $