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.
Read more about this topic: Integral
Other articles related to "fundamental theorem of calculus, theorem":
... Fundamental theorem of calculus ... Let f be a continuous real-valued function defined on a closed interval ...
... 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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