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 Important Results on Integration


 



 

14.
 

15.  
 

16.  

 

17.
 

18.

 

19.

 

20.
 

Properties of definite integration

 

1.  Change of variable does not change the value of integral



 

 


 

2.  Interchange of limits changes the sign of integral



 

 


 

3.  Any definite integral can be expressed as the sum of any number of definite integrals by splitting the range of integration




 

 


 

4.  When the lower limit is zero, the integral f(x) can be changed to f (a–x) where a is upper limit



 

 


 

5.  When f (x) = f (a + x)




 

 

 

6. 

 

            

 

 


       

7.    

 

 

 

 

8.    
 

        = 0 

 

 





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