求定积分∫ (arcsinx)^2dx.上限1,下限0

问题描述:

求定积分∫ (arcsinx)^2dx.上限1,下限0

令arcsinx = t.∫(arcsinx)²dx {0→1} = ∫t²d(sint) {0→π/2} = t²sint {0→π/2} - 2∫tsintdt {0→π/2} = π²/4 + 2∫td(cost) {0→π/2} = π²/4 + 2tcost {0→π/2} - 2∫costdt {0...