# Lect30 - Antiderivatives Any function F(x with the property...

This preview shows pages 1–4. Sign up to view the full content.

92.131 Lecture 30 1 of 10 Ronald Brent © 2009 All rights reserved. Antiderivatives Any function ) ( x F with the property that ) ( ) ( x f x F = on an interval I is called an antiderivative of ) ( x f on the interval I . Examples: a) 2 3 6 ) ( x x x x F + + = is an antiderivative of x x x x f 2 3 6 ) ( 2 5 + + = , since ) ( ) 2 3 6 ( ) ( ) ( 2 5 2 3 6 x f x x x x x x dx d x F = + + = + + = b) 1 2 3 ) ( 4 + + = t t t D is an antiderivative of t t t d 2 1 6 ) ( 3 + = , since ) ( 2 1 6 1 2 3 ) ( 3 4 t d t t t t dt d t D = + = + + = Note: We usually associate the uppercase-letter function as antiderivative of corresponding lowercase-letter function.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
92.131 Lecture 30 2 of 10 Ronald Brent © 2009 All rights reserved. Theorem 1: If ) ( x F is an antiderivative of ) ( x f on an interval I , and C is any constant, then C x F + ) ( is the most general antiderivative of ) ( x f on I . Finding Formulas for Antiderivatives Let C k x x F k + + = + 1 ) ( 1 , where 1 k is any real number, and C is an arbitrary constant. Then, ) ( x F is an antiderivative for the function k x x f = ) (. Every antiderivative of ) ( x f , where 1 k has this form.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

Lect30 - Antiderivatives Any function F(x with the property...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online