Fundamental Theorem of Calculus

Definition

The Fundamental Theorem of Calculus states that if f(x) is continuous on an interval [a, b] and F(x) is any antiderivative of f(x), then ∫[a,b] f(x) dx = F(b) - F(a). In simpler terms, it relates differentiation and integration by showing that finding the area under a curve can be done by evaluating its antiderivative at two points.

Related terms

Antiderivative:

An antiderivative (also known as an indefinite integral) reverses differentiation and gives us back the original function before it was differentiated.

Definite Integral:

A definite integral is used to find the exact area under a curve between two given points. It is represented by ∫[a,b] f(x) dx, where a and b are the limits of integration.

Riemann Sum:

A Riemann sum is an approximation of the area under a curve using rectangles. It involves dividing the interval into subintervals and evaluating the function at specific points within each subinterval.