I know the value of the following definite integral
I also have a realtion
i.e. x is an explicit function of y but I do not have y as an explicit
function of x. The relation between x and y is generally non linear.
Now I want to get the following definite integral
i.e. multiplied by x evaluated over the interval [a,b].
Is there an analytic (not numeric) way to evaluate this integral using
for example mean value or similar averaging technique?