I want to know the meaning of Semidefinite Integral.

I am used to read definite and indefinite integral but I want to know the meaning of such equation :

$\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\right]\right) \left(a+\frac{\int_{-\frac{a}{\pi(e)}}\mu f(\mu)d\mu }{\left(1-F\left[-\frac{a}{\pi(e)}\right]\right)}\right)$

Where :

$\pi(e):$ is the probability of finding the information $\mu$ depending of the effort $e$ of the agent. $\left(1-F\left[-\frac{a}{\pi(e)}\right]\right)$ is the condition for the agent to search this information depending on the parameter $a$ which can be viewed as a reward.

$\mu$ is a stochastic term distributed by $f(\mu)$, the expected value of $\mu$ is 0.

I do not understand the second term of the equation where there is only the lower bound: $\int_{-\frac{a}{\pi(e)}}\mu f(\mu)d\mu$


1 Answer 1


It is just an opaque way to denote that the non-definite integration limit will take the value of the variable itself. Namely,

$$\int_a g(x) dx \equiv \int_a^x g(s)ds$$

... where $s$ is just the dummy variable of integration. Since sometimes we use the notation $\int _D f(x) dx$ to denote fully definite integration "over the domain $D$ of $x$", I would avoid the left-hand side notation and I would stick with the more clear right-hand-side one.

I do hope that the authors where you find this notation mean what I wrote above, because this is what mathematicians mean by it.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.