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,

Recommended Links
vector functions
operations with vector functions
limits and continuity of vector functions
graphs of vector functions
vector differentiation
tangent vectors
smooth curves
derivative rules
vector integration
motion of an object
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curvature

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Thomas' Calculus, Early Transcendentals, Media Upgrade (11th Edition)
Thomas' Calculus, Media Upgrade (11th Edition)
Thomas' Calculus Early Transcendentals; Student's Solutions Manual; Part One
Calculus (With Analytic Geometry)(8th edition)
Calculus (Stewart's Calculus Series)
Applied Calculus
Calculus Textbooks
Elementary Calculus
Advanced Calculus
Supplementary Resources


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