When solving a integral problem domain $[x_1,x_2]$, I start with writing down this: $$\int_{x_1}^{x_2} f(x) dx = F(x_2) - F(x_1).$$ Then I calculate the $F(x)$ and fill in the respected $x_1$ and $x_2$.
But when the function in the problem given starts already is capitalized: $T(x) = 2x$. How do I write down the integral function? $$\int_{x_1}^{x_2} T(x) dx = T(x_2) - T(x_1),$$ simply looks stupid.
Isn't there an similar symbol like the one used for the derivative, the apostrophe ( ' )?
Any ideas?
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$\begingroup$I'd write "$\int_a^b T(x)~ dx = U(b) - U(a)$, where $U$ is any antiderviative of $T$."
In fact, in what you've proposed as your "standard" method, it'd probably be a good idea to mention that "$F$ is an antiderivative of $f$" as well, and not rely on other folks heaving learned the same typographical conventions as those used by your teacher or textbook author.
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