求定积分∫0～1【 y(1-y）】^1/2dy 望大神指教

Answer 1

=∫√(1/4-(y-1/2)²)dy，换元y=1/2+sinu/2
=∫(-π/2到π/2)cosu/2*cosu/2du
=1/8∫(1+cos2u)du
=u/8+sin2u/16
=π/8