MATH 140 Lecture Notes - Lecture 22: Differential Calculus, Antiderivative
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Definition: x is a continuous function on where a, b] and (x) g f varies f(t) dt x a. If we let x vary, the number denoted by (x)g x a g depends only on x x is a fixed number, then the integral. , which appears as the variable is a definite f(t) dt x a f(t) dt also varies and defines a function x. The fundamental theorem of calculus, part 1: if f function g defined by (x) g f(t) dt where a x b is continuous on a, b] is continuous on a, b] and. Using leibniz notation for derivatives, this can be written as when f is continuous x dx d a f(t) dt f(x) x a g (x) , which says that if f is (x) g x dx d a integrated and then the result is differentiated, we arrive back at the original function of f f(x) dx.
