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Published On:Friday 16 December 2011
Posted by Muhammad Atif Saeed

Integration by the Substitution method(or 'changing the variable')


This is best explained with an example:
substitution problem#1
Like the Chain Rule simply make one part of the function equal to a variable eg u,v, t etc.
substitution variable
Differentiate the equation with respect to the chosen variable.
substitution derivative
Rearrange the substitution equation to make 'dx' the subject.
substitution rearrange
Substitute for 'dx' into the original expression.
substitution dx
Substitute the chosen variable into the original function.
substitute chosen variable
Integrate with respect to the chosen variable.
integrate with respect to t
Restate the original expression and substitute for t.
final equation
NB Don't forget to add the Constant of Integration(C) at the end. Remember this is an indefinite integral.



Example #1
substitution problem#1



Example #2
substitution problem#2

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Example #3
substitution problem#3

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Posted by Muhammad Atif Saeed on 13:00. Filed under . You can follow any responses to this entry through the RSS 2.0. Feel free to leave a response

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I am doing ACMA from Institute of Cost and Management Accountants Pakistan (Islamabad). Computer and Accounting are my favorite subjects contact Information: +923347787272 atifsaeedicmap@gmail.com atifsaeed_icmap@hotmail.com

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