Vector Integration

     Since integration is a linear process, studying vector functions and integration together is natural. Indeed recall that with functions of one variable, definite integration is the process of taking a limit of a Riemann sum. Basically, since taking limits and Riemann sums both are linear processes, so is integration.

Definition (Indefinite Integral of a Vector Function) Let  

,

where , , and are continuous on the closed interval Then the indefinite integral of is

Example (Indefinite Integral of a Vector Function) Compute



    Solution. We have,





where is a constant vector.

Definition (Definite Integral of a Vector Function) Let

,

where , , and are continuous on the closed interval Then the definite integral of is the vector  

Example (Definite Integral of a Vector Function) Given the vector function



Find the value of for which

    Solution. We have,
    
  


  
Thus, and So,

• print this page
• pages linking here
• related pages

Cite this as:
Vector Integration
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/vector-integration.html