Solution
= Solution
Choose the overall <phase> so that $A$ is positive. <Normalization> requires
$$
1=|A|^2\int_{-a}^a(a^2-x^2)^2dx
=|A|^2\frac{16a^5}{15}.
$$
Therefore
$$
\boxed{A=\frac{\sqrt{15}}{4a^{5/2}}.}
$$
An arbitrary constant <phase> multiplying this answer has no effect on any expectation value.