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Improper Integral

Improper Integral

A definite integral for which the integrand has a discontinuity between the bounds of integration, or which has ∞ and/or –∞ as a bound. Improper integrals are evaluated using limits as shown below. If the limit exists and is finite, we say the integral converges. If the limit does not exist or is infinite, we say the integral diverges.

 

Two examples of improper integrals evaluated with limits: ∫(1 to ∞) dx/x²=1 and ∫(-∞ to ∞) dx/(x²+1)=π

Evaluation of improper integral ∫₁³ dx/(x−2)^(2/3) using limits, splitting at discontinuity x=2, result equals 0.

 

 

See also

Integral test