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Mathematics
Mathematics
Problem
Explain why the improper integral
∫
1
∞
1
x
2
d
x
\displaystyle \int_{1}^{\infty} \frac{1}{x^{2}}\,dx
∫
1
∞
x
2
1
d
x
converges, whereas
∫
1
∞
1
x
d
x
\displaystyle \int_{1}^{\infty} \frac{1}{x}\,dx
∫
1
∞
x
1
d
x
diverges.
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