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∫dx/x^2在1到正无穷的定积分,
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∫dx/x^2在1到正无穷的定积分,
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答案和解析
∫(1/x²)dx
=lim[b→+∞] ∫(1/x²)dx
=lim[b→+∞] ∫(x^-2)dx
=lim[b→+∞] x^(-2+1)/(-2+1)
=lim[b→+∞] (-1/x)
=lim[b→+∞] (-1/b)-(-1/1)
=lim[b→+∞] (-1/b)+1
=-1/∞+1
=1
=lim[b→+∞] ∫(1/x²)dx
=lim[b→+∞] ∫(x^-2)dx
=lim[b→+∞] x^(-2+1)/(-2+1)
=lim[b→+∞] (-1/x)
=lim[b→+∞] (-1/b)-(-1/1)
=lim[b→+∞] (-1/b)+1
=-1/∞+1
=1
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