Question

hi everyone. I am interested in evaluating the integral of an integral, using integration by parts. the problem is : dg/dx = integral(F(x,g)dt) (from a to x). it is written somewhere that g(x) = integral((x-t)F(x,g)dt) (from a to x) + c Thanks in advance.

Answer 1

so you're just integrating twice?

Answer 2

or are you doing a double integral?

Answer 3

the problem is : dg/dx = integral(F(x,g)dt) (from a to x). it is written somewhere that g(x) = integral((x-t)F(x,g)dt) (from a to x) + c
\[\frac{ dg }{ dx }=\int\limits_{a}^{x}F(x,g(t))dt\]
solution is
\[g(x)= c + \int\limits_{a}^{x}(x-t)F(x,g(t))dt\]

Answer 4

I appreciate any answer to steps of the above solution.