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Integration by Parts: Integration Constants

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First published at 18:56 UTC on July 27th, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over a very interesting video on the concept of integration constants that arise for all integrals. Basically an integral can be viewed as the anti-derivative of a function and thus the derivative of that anti-derivative would make an constant go to zero because the derivative of a constant is zero. This means that an integral can have many different solutions because the constant can be any number. This concept is used in my earlier video on the proof of the trapezoidal rule error bound formula for integral approximation. In that proof I show how we can add these extra integration constants when using the method of integration by parts to make the integral appear in a specific way we want to for the proof because the constants themselves cancel out and thus aren't changing the value of the resulting integral. This is a very interesting video and understanding the concept of integration concept has wide reaching effects so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIheVcfp45EAEdRovO_g

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/integration-by-parts-integration-constants

Related Videos:

Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk
Integrals and AntiDerivatives - Area Example: http://youtu.be/Q2PTVZBzMWQ
Integration by Parts: Proof: http://youtu.be/TZhEOct5u_M .

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