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Lecture

7.3 Trigonometric Substitution: Overview

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Department
Mathematics
Course Code
MAT136H1
Professor
all

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7.3 Integration Techniques
Trigonometric Substitution: Overview
Integrals in the form of   are used to find the area of circle or ellipse.
For the expression  , the identity      is used for    substitution.
For the expression  , the identity      is used for     substitution.
For the expression  , the identity     is used for     substitution.
After solving the integral using trigonometric substitutions, substituted variable must be replaced by the
original variable. Based on Pythagorean Theorem, all sides of the right triangle is defined, and THE
substituted variable is replaced by the original variable based on the right triangle.
Half-Angle Formula
 
 

  
Double-Angle Formula
    
          
    

Addition & Subtraction Formula
       
       
        
        
    
   
    
   

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Description
7.3 Integration Techniques Trigonometric Substitution: Overview Integrals in the form o∫ √ are used to find the area of circle or ellipse. For the expression √ , the identity is used for substitution. For the expression √ , the identity is used for substitution. For the expression √ , the identity is used for substitution. After solving the integra
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