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Improper Integrals: Example 10: Comparison Theorem

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First published at 23:17 UTC on May 22nd, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over another example on using the comparison theory to determine if an improper integral is convergent or divergent. The example I cover is the integral of the function (1+e^(-x))/x from x = 1 to x approaching infinite. This function is very simple to the integral I solved in my Example 1 video about the integral of the function 1/x. As I showed in that earlier video, that integral diverges and I show in this video that (1 + e^(-x))/x is always greater than 1/x which according to the comparison theory makes that integral diverge as well.

Download the notes in my video: http://1drv.ms/1P5RvJB

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-10-comparison-theorem

Related Videos:

Improper Integrals: Example 9: Comparison Theorem: https://youtu.be/NRKNOqSyh_Q
Comparison Theorem for Type 1 Improper Integrals: https://youtu.be/SswR3u6rurU
Can We Integrate All Continuous Functions?: http://youtu.be/OFEDLJYqYps
Improper Integrals: Type 2: Discontinuous Integrands: https://youtu.be/livlGUBuM54
Improper Integrals: Type 1: Infinite Intervals: https://youtu.be/9ZlsCy3wdZU
Improper Integrals: Introduction: https://youtu.be/ud44W-0jC-c
Improper Integrals: Example 1: Divergent Sum: https://youtu.be/6b_zaerpudo .

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