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If  f ,  g : [ a ,  b ] →  are two continuous functions, then there exists a point  c  ∈ ( a ,  b ) such that ∫ a c f ( x ) d x + ( c - a ) g ( c ) = ∫ c b g ( x ) d x + ( b - c ) f ( c ) . \int_a^c {f\left(x \right)} dx + \left({c - a} \right)g\left(c \right) = \int_c^b {g\left(x \right)} dx + \left({b - c} \right)f\left(c \right). In this paper, we study the approaching of the point  c  towards  a,  when  b  approaches  a.

Calculus for the intermediate point associated with a mean value theorem of the integral calculus