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:
“Nonwhite and working-class women, if they are ever to identify with the organized women’s movement, must see their own diverse experiences reflected in the practice and policy statements of these predominantly white middle-class groups.”
—Kimberly Crenshaw (b. 1959)
“He admired the terrible recreative power of his memory. It was only with the weakening of this generator whose fecundity diminishes with age that he could hope for his torture to be appeased. But it appeared that the power to make him suffer of one of Odette’s statements seemed exhausted, then one of these statements on which Swann’s spirit had until then not dwelled, an almost new word relayed the others and struck him with new vigor.”
—Marcel Proust (1871–1922)