fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of differentiation with integral. It contains two parts.

The first fundamental theorem of calculus states that for a continuous function , the antiderivative can be obtained as the integral of over an interval with a variable upper bound.

If is continuous on then

is continuous on and differentiable on and,

The second fundamental theorem of calculus states that the integral of a function over a fixed interval is equal to the change of any antiderivative between the endpoints.

Suppose is a continuous function on and suppose that is an antiderivative for . Then,

See Also

• fundamental theorem of calculus for line integrals