Integral - Fundamental Theorem of Calculus - Statements of Theorems

Statements of Theorems

  • Fundamental theorem of calculus. Let f be a continuous real-valued function defined on a closed interval . Let F be the function defined, for all x in, by

Then, F is continuous on, differentiable on the open interval (a, b), and

for all x in (a, b).

  • Second fundamental theorem of calculus. Let f be a real-valued function defined on a closed interval that admits an antiderivative g on . That is, f and g are functions such that for all x in ,

If f is integrable on then

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