Page 25 - Integration Problems
P. 25

Example 5:

        Perform the integration


                                    2
                                           2  
                                   ∫               
                                      1 +      
                                   1



        Make the substitution,


                                                   
                                      = 1 +   
        Then


                                                                
                                  
                           =         ,       or            =
                                                                  

        The integral becomes,

                   2
                          2             2     2            2       
                 ∫                 = ∫         .     = ∫             
                    1 +                1                  1     
                 1
                                                
                               
        Since    = 1 +    ,     then       =    − 1
        The integral becomes,


                                     2     − 1
                                  ∫                 
                                    1       

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