Find the value of a≥0 that maximizes the integral from 0 to a of (4-x²)dx.

Question

Thank you!

Answer 1

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.