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Tuesday, January 1, 2013

Integration - Algebraic Substitution, Parts

Category: Integral Calculus

"Published in Suisun City, California, USA"

Evaluate

Solution:

Consider the given equation



If 
then



Substitute the values of x and dx to the given equation, we have







Since there are two functions in the integration and we cannot integrate by simple integration, then we have to integrate the above equation by integration by parts, as follows



Let


and



Substitute the values to the integration by parts formula, we have









but 

Therefore,