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?$(acontent)
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![求定积分:{(x的2次方)乘以[根号下(1减去x的2次方)]}dx,上限是1,下限是0?$(acontent)](/uploads/image/z/1055516-68-6.jpg?t=%E6%B1%82%E5%AE%9A%E7%A7%AF%E5%88%86%3A%7B%28x%E7%9A%842%E6%AC%A1%E6%96%B9%29%E4%B9%98%E4%BB%A5%5B%E6%A0%B9%E5%8F%B7%E4%B8%8B%281%E5%87%8F%E5%8E%BBx%E7%9A%842%E6%AC%A1%E6%96%B9%29%5D%7Ddx%2C%E4%B8%8A%E9%99%90%E6%98%AF1%2C%E4%B8%8B%E9%99%90%E6%98%AF0%3F%24%28acontent%29)
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