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My favorite theorm is the Fundamental theorem of Calculus because in calculus it seem to sum up everything that we learned. | My favorite theorm is the Fundamental theorem of Calculus because in calculus it seem to sum up everything that we learned. | ||
| − | + | The fundamental theorem of Caluculus part one states Let f be a continuoues real function defined on a closed interval [a,b]. Let F be the function for all x in [a,b] by F(x)=Integral from a to x of f(t) dt. Then F is continuous on [a,b] and differental on the open interval (a,b) and F'(x)=f(x) for all x in (a,b). | |
Part Two states Let f be a continuous real function defined on a closed interval [a, b]. Let F be an antiderivative of f, for all x in [a, b], Then the integral from a to b of f(x) dx equals F(a)-F(b). | Part Two states Let f be a continuous real function defined on a closed interval [a, b]. Let F be an antiderivative of f, for all x in [a, b], Then the integral from a to b of f(x) dx equals F(a)-F(b). | ||
Latest revision as of 15:00, 1 September 2008
My favorite theorm is the Fundamental theorem of Calculus because in calculus it seem to sum up everything that we learned. The fundamental theorem of Caluculus part one states Let f be a continuoues real function defined on a closed interval [a,b]. Let F be the function for all x in [a,b] by F(x)=Integral from a to x of f(t) dt. Then F is continuous on [a,b] and differental on the open interval (a,b) and F'(x)=f(x) for all x in (a,b).
Part Two states Let f be a continuous real function defined on a closed interval [a, b]. Let F be an antiderivative of f, for all x in [a, b], Then the integral from a to b of f(x) dx equals F(a)-F(b).
