posted by Shelby .
Find the value of a≥0 that maximizes the integral from 0 to a of (4-x²)dx.
You have Int[f(x)] = F(a)
To maximize F(a), you want its derivative f(a) to be zero.
4-a^2 = 0 when a = -2 or 2
Knowing what you do about cubics, you know the max on [0,4] will occur at a = 2.