I need to evaluate the following integral:
Integral_0_1 f(y)*Integral_0_y g(x) dx dy
where e.g.
Integral_a_b g(x) dx
is the definite integral of f(x) over x= a,b.
In the case of the functions I am working with, there is no closed form solution to the integral of g(x), so I need to evaluate this integral numerically.
NIntegrate[f(y)*NIntegrate[g(x),{x,0,y}],{y,0,1}]
this results in an error message stating that x=y is not a valid limit of integration, because the inner Nintegrate function recognizes y as a variable rather than a numerical value assigned to it. What are my options for numerically integrating functions of this type, i.e. where
Integral_0_y g(x) dx = F(y)
cannot be computed explicitly but is part of the integrand? I've attached a notebook (with an example) in case my notation isn't clear. The numerical integration evaluates to something, but I'm not confident that the result is meaningful because of the error in having a variable y as the integrand.
