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

Read more about this topic:  Integral, Fundamental Theorem of Calculus

Famous quotes containing the words statements of and/or statements:

    The wise man regulates his conduct by the theories both of religion and science. But he regards these theories not as statements of ultimate fact but as art-forms.
    —J.B.S. (John Burdon Sanderson)

    There is a certain embarrassment about being a storyteller in these times when stories are considered not quite as satisfying as statements and statements not quite as satisfying as statistics; but in the long run, a people is known, not by its statements or its statistics, but by the stories it tells.
    Flannery O’Connor (1925–1964)