0
$\begingroup$

I have the following simple multiplication of integral by itself:

$$\int_{0}^{x}a(t)dt\int_{0}^{x}a(t)dt$$

I feel that I probably miss something very basic, but is it possible to write it in some form like:

$$\int_{0}^{x}f(a(t),t)dt$$

I faced this integral in integral equation and was surprised when didn't find literature handling this, so I guess easy transformation must exists.

$a(t)$ is a very general differentiable function.

$\endgroup$
1
$\begingroup$

First of all you are abusing the notation, since the variable you are integrating over and the limits are the same variable $t$.

And to address your question (assuming your notation is fixed), yes, you can where $$f(a(t),t) = a(t) \int_0^x a(y)dy$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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