Integral of inverse functions

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, <a href="/facts/Integrals/V7lyV997">integrals</a> of <a href="/facts/Inverse_functions/Tg5nnXlu">inverse functions</a> can be computed by means of a formula that expresses the <a href="/facts/Antiderivative/5qDsudIv">antiderivatives</a> of the inverse 
  
    
      
        
          f
          
            −
            1
          
        
      
    
    {\displaystyle f^{-1}}
  
 of a <a href="/facts/Continuous_function/sKbl02pB">continuous</a> and <a href="/facts/Inverse_functions/Tg5nnXlu">invertible function</a> 
  
    
      
        f
      
    
    {\displaystyle f}
  
, in terms of 
  
    
      
        
          f
          
            −
            1
          
        
      
    
    {\displaystyle f^{-1}}
  
 and an antiderivative of 
  
    
      
        f
      
    
    {\displaystyle f}
  
.  This formula was published in 1905 by <a href="/facts/Charles-Ange_Laisant/UQIgH2Lg">Charles-Ange Laisant</a>.
</p>

Integral of inverse functions open-in-new

Integral of inverse functions