MATH 111 Lecture 20: Integrals Part1
13 Jul 2015
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A function f is the antiderivative of f on an interval i if f (x) = f (x) for all x in i. If f is an antiderivative of f on an interval i, then the most general derivative of f on i is. The derivative of the answer should equal the original function. 1/x ex cos x sin x sec2x sec x tan x. Particular antiderivative (xn+1)/ (n+1) ln |x| ex sin x. Cos x tan x sec x sin -1x tan-1x. For non-particular antiderivatives, add the constant c to the end. Ex: antiderivative of ex = ex + c. F(x) dx = f (x) means that f (x) = f(x) Another notation for antiderivatives, called an indefinite integral. There is a difference between indefinite and definite integrals. Indefinite: f(x) dx means an integral on the interval (a,b) Indefinite integrals follow all of the same rules as antiderivatives, with one addition.
