6533b7ddfe1ef96bd1273c51

RESEARCH PRODUCT

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

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Abstract 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.