Unizor - Definite Integrals - Improper Integrals Examples 1
Channel: Zor Shekhtman on UNIZOR Education
Date: 2017-05-16

Unizor - Creative Minds through Art of Mathematics - Math4Teens

Notes to a video lecture on http://www.unizor.com

Improper Definite Integrals

Example 1.1

∫[0,1]1/√x dx = lim[a→0] ∫[a,1]1/√x dx
Answer: 2

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Example 1.2

∫[0,∞]e^(−x) dx = lim[b→∞] ∫[0,b]e^(−x) dx
Answer: 1

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Example 1.3

∫[0,∞]1/(1+x²) dx = lim[b→∞] ∫[0,b]1/(1+x²) dx
Answer: π/2

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Example 1.4

∫[1,∞](1/x²)·e^(1/x) dx = lim[b→∞] ∫[1,b](1/x²)·e^(1/x) dx
Answer: e −1