# Expressing a definite integral as pure function with the upper-bound as it argument

Suppose i have an integral which has a closed form,

$\quad \quad \int_{a}^{b} f(x) dx=F(a,b)$

I want to use output function $F$ as a pure function, like F[a,#]& so i try the following:

Integrate[f[x], {x, a, #}]&;


but this does not evaluate the integral before setting it as a pure function. So I tried the following:

Integrate[f[x], {x, a,b}];
(% /. {b -> #})&;


but this doesnot evaluate the last result variable %. So I also tried the following to no success:

Integrate[f[x], {x, a, #}]
Function[%];


In the maple programming language there is a command "unapply" which evaluates the definition of the function before assigning the arrow operator to it. Is there any equivalent to this in Mathematica? (I am new to Mathematica)

## 1 Answer

Not sure how general solution you want but you can do something like:

Evaluate[Integrate[f[x], {x, a, b}] /. b -> (#)] &

• Thank you that's general enough for me. Apr 18, 2015 at 18:52