Vault Of Euclid

Divergence of the Integral of 1/x^2 from 0 to 1

Integrals warmup

Investigate \( \int_{0}^{1} \frac{1}{x^{2}} \, dx \).
improper-integraldivergenceinfinite-discontinuitylimitpower-rulefundamental-theorem-of-calculusevaluate-integralcalculus-iintegrationone-sided-limitvertical-asymptoterational-function

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What you need first

What this problem tests

Tests the ability to identify an improper integral due to a vertical asymptote and correctly apply the limit definition to determine divergence.

This is a standard introductory example in Calculus II when learning about improper integrals of the second kind (infinite discontinuities).

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