求定积分:{(x的2次方)乘以[根号下(1减去x的2次方)]}dx,上限是1,下限是0?$(acontent)

求定积分:{(x的2次方)乘以[根号下(1减去x的2次方)]}dx,上限是1,下限是0?$(acontent)
求定积分:{(x的2次方)乘以[根号下(1减去x的2次方)]}dx,上限是1,下限是0?
$(acontent)

求定积分:{(x的2次方)乘以[根号下(1减去x的2次方)]}dx,上限是1,下限是0?$(acontent)
[0,1] ∫ x²√(1+x²) dx
= 1/8 [ -2x(1-x²)^(3/2) + x√(1-x²) + arcsinx ] | [0,1]
= 1/8 arcsin1
= π/16