Posted by **Shelby** on Sunday, October 2, 2011 at 10:55pm.

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

Thank you!

- Calculus -
**Steve**, Monday, October 3, 2011 at 5:57am
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.

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