The smallest value of \[I(a) = \displaystyle\int_0^1 \! (x^2 - a)^2 \, \mathrm{d}x,\] as \(a\) varies, is
\(\frac{3}{20}\),
\(\frac{4}{45}\),
\(\frac{7}{13}\),
\(1\).
Calculus of Powers
Question
The smallest value of \[I(a) = \displaystyle\int_0^1 \! (x^2 - a)^2 \, \mathrm{d}x,\] as \(a\) varies, is
\(\frac{3}{20}\),
\(\frac{4}{45}\),
\(\frac{7}{13}\),
\(1\).