Improper Integrals: Example 7: IMPORTANT Example

In this video I go over another example on improper integrals and this time evaluate the integral of the function 1/(x - 1) from x = 0 to x = 3. This is a very important example because it illustrates the need to always check the function being integrated to see if it is continuous or discontinuous in the interval being integrated. In this particular example there is a vertical asymptote at x = 1 so we must treat this as an improper integral of type 2 and evaluate it accordingly. In this example, I show how this integral diverges to negative infinite so the integral does not exist as a definite number. If I had not noticed that vertical asymptote and instead solved it like a regular integral the answer would have yielded the number ln(2) which is wrong! So make sure to always check if you are dealing with a proper or improper integral before you start evaluating the integral.

Download the notes in my video: http://1drv.ms/1U2vvqF

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-7-important-example

Related Videos:

Improper Integrals: Example 6: sec(x): https://youtu.be/yHnv2w9OVWk Improper Integrals Example 5: 1/sqrt(x-2): https://youtu.be/C8X_TUdTo-A Improper Integrals: Type 2: Discontinuous Integrands: https://youtu.be/livlGUBuM54 Improper Integrals: Introduction: https://youtu.be/ud44W-0jC-c The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ Integration by Parts: Example 2: ln(x): http://youtu.be/wVjra6DCZzE .

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=MbjghfT0IoM