Explain this a little plz well i have another problem with finding a(some) functions. The problem is this: FInd all non-negative continuous functions f:-->R that fullfil the following: integ from 0 to 1 of f(x)dx =1 integ from 0 to 1 of xf(x)dx=a and integ from 0 to 1 of x^2 f(x)dx=a^2 where a is an element of the reals. this problem is in a textbook, and it starts like this integ from 0 to one of (x-a)^2 f(x) dx, and at the end comes to a contradiction, hence it concludes that such a functions does not exist. My question is what is really this problem asking? SO if you could explain a little to me how should i start thinking about this problem? Because i want to fully understand what i am writing, and why am i writing something. So could anyone please elaborate this problem a little for me??? I really thank all you guys for your time, and for taking the effort on helping us all. P.S. Btw it is not homework, just a problem i encountered in the textbook.