Question 61
Consider $a \in (0,1)$ and $C$ the set of all increasing functions $f: [0,1] \to [0, \infty)$, such that $\int_0^1 f(x) dx = 1$. Determine:
a. $\max_{f \in C} \int_0^a f(x) dx$,
and
b. $\max_{f \in C} \int_0^a (f(x))^2 dx$.
a. $\max_{f \in C} \int_0^a f(x) dx$,
and
b. $\max_{f \in C} \int_0^a (f(x))^2 dx$.