Rules of Integration for Definite Integral

In order to simplify the task of finding integrals, some general rules are developed to help finding definite integrals with having to use the definition directly.

Definite Integral Properties

Some useful properties of definite integrals

1. Definite integral as limit of function sum

   

   Proof:

   

2. additivity of intervals

   

   Proof:

   

3. zero length of interval

   

   Proof:

   

4. reversing of limits

   

   Proof:

   

5. subtraction of intervals

   

   Proof:

   

6. Constant Multiple Rule of definite integral

   

   Proof:

   

7. Constant Multiple Rule of Identity function of definite integral

   

   Proof:

   

8. Constant Rule of zero function of definite integral

   

   Proof:

   

9. Sum of Functions Rule of definite integral

   

   Proof:

   

10. Difference of Functions Rule of definite integral

    

    Proof: