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.
* * *
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 (
Newton, Sir Isaac) and Gottfried Wilhelm Leibniz (
Leibniz, Gottfried Wilhelm).
* * *
Universalium.
2010.
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