Limits of integration

In <a href="/facts/Calculus/MEmUTYoz">calculus</a> and <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a> the limits of integration (or bounds of integration) of the <a href="/facts/Integral/V7lyV997">integral</a>

∫
          
            a
          
          
            b
          
        
        f
        (
        x
        )
        
        d
        x
      
    
    {\displaystyle \int _{a}^{b}f(x)\,dx}

of a <a href="/facts/Riemann_integral/vWGrPhVh">Riemann integrable</a> <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> 
 
 
 
 f
 
 
 {\displaystyle f}
 
 defined on a <a href="/facts/Closed_set/upYnRTUj">closed</a> and <a href="/facts/Bounded_set/yCldjtoy">bounded</a> interval are the <a href="/facts/Real_number/R02gw5Pb">real numbers</a> 
 
 
 
 a
 
 
 {\displaystyle a}
 
 and 
 
 
 
 b
 
 
 {\displaystyle b}
 
, in which 
 
 
 
 a
 
 
 {\displaystyle a}
 
 is called the lower limit and 
 
 
 
 b
 
 
 {\displaystyle b}
 
 the upper limit. The region that is <a href="/facts/Bounded_set/yCldjtoy">bounded</a> can be seen as the area inside 
 
 
 
 a
 
 
 {\displaystyle a}
 
 and 
 
 
 
 b
 
 
 {\displaystyle b}
 
.
For example, the function 
 
 
 
 f
 (
 x
 )
 =
 
 x
 
 3
 
 
 
 
 {\displaystyle f(x)=x^{3}}
 
 is defined on the interval 
 
 
 
 [
 2
 ,
 4
 ]
 
 
 {\displaystyle [2,4]}

∫
          
            2
          
          
            4
          
        
        
          x
          
            3
          
        
        
        d
        x
      
    
    {\displaystyle \int _{2}^{4}x^{3}\,dx}

with the limits of integration being 
 
 
 
 2
 
 
 {\displaystyle 2}
 
 and 
 
 
 
 4
 
 
 {\displaystyle 4}
 
.

Limits of integration open-in-new

Limits of integration