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).
