MATH 1A Lecture Notes - Lecture 26: Antiderivative
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Math 1a - lecture 26 - 5. 4 indefinite integrals and 5. 5 substitution rule. The definite integral b a f ( x) dx is a number, defined using limit of riemann sums. Last time we saw that if f ( x) is continuous on. , then b a f ( x) dx=f (b) f ( a) where f ( x) is any anti-derivative of f ( x) We define the indefinite integral not by riemann sums, but as an anti-derivative of can be either an arbitrary anti-derivative: f ( x ) Or a specific one: x a f ( x) dx=f ( x) f (a) , where f (a) is a specific choice of c . Note: for definite integral, ftc assumes is continuous on integral, we defined it on one connected interval of the domain of f ( x ) For indefinite at a time. f ( x) is continuous on x>0 and x<0 , but not at x=0 .
