Question

If `P:RR->RR` verify this equality:`P(1)+...+P(n)=n^5;n=1,2,...`,then how to find value of `int_0^1P(x)dx`?

Answer 1

See below.

Explanation:

Considering that the problem is:

`P(1/n)+P(2/n)+ cdots+P(k/n)+ cdots+P((n-1)/n) + P(1) = n^5`

In this case we have

`lim_(n->oo)sum_(k=1)^n (P(k/n))/n = int_0^1P(xi) d xi = lim_(n->oo)n^4=oo^4=oo`