Improper Integrals: Example 8: ln(x)

In this video I go over another example on improper integrals and this time solve the integral of the function ln(x) from x = 0 to x = 1. In this example it is important to note that ln(x) approaches infinity as x approaches 0 from the right side. This makes it an improper integral of type 2 because of the resulting infinite discontinuity or vertical asymptote. Thus in solving this example we need to write it as a limit of a definite integral from x = t to x = 1 as t approaches 0 from the right side. We can also integrate the function ln(x) by using integration by parts and evaluating the resulting limit by using L'Hospital's Rule to get the result that the integral converges to the value -1.

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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 L'Hospital's Rule and Indeterminate Forms - Intro: http://youtu.be/x-djc6wrY5w .

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