The *fundamental theorem of calculus* is the statement that differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved. An important consequence, sometimes called the *second fundamental theorem of calculus*, allows one to compute integrals by using an antiderivative of the function to be integrated.

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### Other articles related to "fundamental theorem of calculus, theorem":

**Fundamental Theorem of Calculus**- Statements of Theorems

... Fundamental theorem of calculus ... Let f be a continuous real-valued function defined on a closed interval ...

**Fundamental Theorem Of Calculus**- Generalizations

... Part I of the

**theorem**then says if f is any Lebesgue integrable function on and x0 is a number in such that f is continuous at x0, then is differentiable for x = x0 with F′(x0) = f(x0) ... On the real line this statement is equivalent to Lebesgue's differentiation

**theorem**... In higher dimensions Lebesgue's differentiation

**theorem**generalizes the

**Fundamental theorem of calculus**by stating that for almost every x, the average value of a function f over a ball of radius r centered at x ...

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