(adsbygoogle = window.adsbygoogle || []).push({}); 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:[01]-->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.

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# Explain this a little

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