<Dl> <Dd> f (x) = ∫ a x h (y) d y and g ′ (x) = 1 . (\ displaystyle f (x) = \ int _ (a) ^ (x) \ h (y) \, dy (\ text (and)) g' (x) = 1 \ .) </Dd> </Dl> <Dd> f (x) = ∫ a x h (y) d y and g ′ (x) = 1 . (\ displaystyle f (x) = \ int _ (a) ^ (x) \ h (y) \, dy (\ text (and)) g' (x) = 1 \ .) </Dd> <P> Which gives the result . </P> <P> For application to principal - value integrals, see Whittaker and Watson, Gakhov, Lu, or Zwillinger . See also the discussion of the Poincaré - Bertrand transformation in Obolashvili . An example where the order of integration cannot be exchanged is given by Kanwal: </P>

When do you change the order of integration