MATH 121 Lecture Notes - Lecture 22: Antiderivative, Power Rule

• School: University of Alabama
• Department: MATH
• Course: MATH 121
• Professor: Wein

Document Summary

In this section we will be given the derivative and we will want to find an equation that has that derivative. If f"(x)=f(x), then f(x) is an antiderivative of f(x). Notice that f, g, h have the same derivative but their equations differ by a constant. The family of antiderivatives is indicated by the notation: Is called an integration symbol. is called differential w. r. t x, which tells you the variable you are trying to integrate. Note: and appear together as a pair. (cid:4666)(cid:4667) is called the integrand function. Power rule: for any real number n -1. , where c is the constant of integration and denotes a real number. took the derivative you subtracted 1 from the power---you now want to add back. You also multiplied by the original power we now want to divide by the new power) dxxfk. Example 1: find the antiderivative of each: dx3 b) . Sum or difference rule: xf xg dx dxxf dxxg.