Ch. 4, 5 - Area and Integration Concepts

These flashcards cover key vocabulary and concepts related to area and integration as discussed in lecture notes.

Area Under a Graph

The total space enclosed by the graph of a function and the x-axis.

Velocity Function v(t)

A function that represents the speed of an object at time t.

Marginal Cost Function MC(x)

A function that represents the cost incurred by producing one additional unit of a good.

Antiderivative

A function F is an antiderivative of f if F' = f.

Definite Integral

An integral that gives the net area under the curve of a function between two specified limits.

Indefinite Integral

An integral that represents a family of functions and includes a constant of integration.

The Fundamental Theorem of Calculus

Links the concept of differentiation and integration, stating that if f is continuous on [a,b], then ∫(f(x)dx) from a to b = F(b) - F(a), where F is any antiderivative of f.

Consumers' Surplus

The difference between what consumers are willing to pay for a good or service versus what they actually pay.

Producers' Surplus

The difference between the amount producers are willing to accept for a good or service versus the actual amount they receive.

Integration by Substitution

A method of integration that involves changing the variable of integration to simplify the integral.

Area Between Two Curves

The space enclosed between two functions f(x) and g(x) over an interval where f(x) ≥ g(x).