Let a, b be positive real numbers.
Prove that
\int_{a \minus{} 2b}^{2a \minus{} b} \left|\sqrt {3b(2a \minus{} b) \plus{} 2(a \minus{} 2b)x \minus{} x^2} \minus{} \sqrt {3a(2b \minus{} a) \plus{} 2(2a \minus{} b)x \minus{} x^2}\right|dx
\leq \frac {\pi}3 (a^2 \plus{} b^2).
Edited by moderator. calculusintegrationinequalitiesgeometrycalculus computations