Techniques of Integration · Improper Integrals
Improper Integral: Type I (Infinite Limit)
When the upper (or lower) limit is infinite, replace it with a variable t and take the limit. If the limit is finite, the integral converges.
- 0 variables
- 2 worked examples
- 16 in Techniques of Integration
Worked examples
Evaluate ∫₁^∞ 1/x² dx.
- lim(t→∞) ∫₁ᵗ x⁻² dx = lim(t→∞) [-1/x]₁ᵗ = lim(t→∞) (-1/t + 1) = 1
Answer: 1 (converges)
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Evaluate ∫₁^∞ 1/x dx.
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Practice
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