fundamental theorem of calculus


fundamental theorem of calculus

Basic principle of calculus. It relates the derivative to the integral and provides the principal method for evaluating definite integrals (see differential calculus; integral calculus). In brief, it states that any function that is continuous (see continuity) over an interval has an antiderivative (a function whose rate of change, or derivative, equals the function) on that interval. Further, the definite integral of such a function over an interval a < x < b is the difference F(b) F(a), where F is an antiderivative of the function. This particularly elegant theorem shows the inverse function relationship of the derivative and the integral and serves as the backbone of the physical sciences. It was articulated independently by Isaac Newton and Gottfried Wilhelm Leibniz.

This entry comes from Encyclopædia Britannica Concise.
For the full entry on fundamental theorem of calculus, visit Britannica.com.

Seen & Heard

What made you look up fundamental theorem of calculus? Please tell us what you were reading, watching or discussing that led you here.

Get Our Free Apps
Voice Search, Favorites,
Word of the Day, and More
Join Us on FB & Twitter
Get the Word of the Day and More