Integral Calculus

Abstract

If x is the level of output and TC is the total cost, then given a cost curve

$$$$

by differentiation the marginal cost curve is

$$$$

That is, by the process of differentiation the total cost function becomes the marginal cost function. If we are now told that a marginal cost function is

$$MC = 6x + 20$$

and asked to determine the total cost function we must reverse the process of differentiation, that is, we must integrate the marginal cost equation. From our knowledge of differential calculus we might guess that

$$TC = 3{x^2} + 20x$$

and we should also realise that there may have been a constant term in the TC function which would have disappeared on differentiation.