MATH 1P97 Lecture Notes - Lecture 9: Function Composition, Power Rule, Antiderivative

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P97
• Professor: Sandra Yee

Document Summary

A function f is an antiderivative of f on an interval i if f"(x) =f(x) for all x in i ( x2) =2x = f ( x) An antiderivative of function f is a function f whose derivative is f. For example, f(x)=x2 is antiderivative of f(x)=2x because. F"(x) = x2 - 4x +1- x3 - 2x2 + x - 1 show that f is an antidertivative of f(x)=x2 - 4x +1 f ( x) Let g be an antiderivative of a function f on an interval i. Then, every antiderivative f of f on i must be of the form f(x)=g(x)+c, where c is constant. The process of finding all antiderivatives of a function is called antidifferentiation or integration. f ( x)dx = f( x)+c (cid:242) 1dx = x +c (cid:242) 2xdx = x2 +k. Rule 1: the indefinite integral of a constant (cid:242) kdx = kx +c (k, a constant) x n+1 +c(n .