Question 71
Let $a\in(0,1)$ and let $\mathcal C$ be the set of increasing functions $f:[0,1]\to[0,\infty)$ such that $\int_0^1f(x)\,dx=1$. Determine:
a. $\max_{f\in\mathcal C}\int_0^af(x)\,dx$,
b. $\max_{f\in\mathcal C}\int_0^a(f(x))^2\,dx$.
a. $\max_{f\in\mathcal C}\int_0^af(x)\,dx$,
b. $\max_{f\in\mathcal C}\int_0^a(f(x))^2\,dx$.