Calculus II Notes 5.4 - Calculus II-Stewart Dr. Berg Spring...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Calculus II- Stewart Dr. Berg Spring 2010 Page 1 5.4 5.4 Indefinite Integrals and the Net Change Theorem Antiderivatives play such an important role in integration that integral notation is commonly used to represent them. Definition f ( x ) dx = F ( x ) means d dx F ( x ) = f ( x ) and is called the indefinite integral of f . Example A cos x dx = sin x + C because d dx sin x + C ( ) = cos x . Notation: In keeping with existing notation and the FTC, f ( x ) dx a b = f ( x ) dx a b . Table of Common Indefinite Integrals c f ( x ) dx = c f ( x ) dx f ( x ) + g ( x ) [ ] dx = f ( x ) dx + g ( x ) dx k dx = kx + C x n dx = x n + 1 n + 1 + C sin x dx = cos x + C cos x dx = sin x + C sec 2 x dx = tan x + C csc 2 x dx = cot x + C sec x tan x dx = sec x + C csc x cot x dx = csc x + C Note: It is understood that each antiderivative is valid only for an interval. Therefore, the general anitiderivative for f ( x ) = 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/28/2010 for the course M 56495 taught by Professor Berg during the Spring '10 term at University of Texas at Austin.

Page1 / 2

Calculus II Notes 5.4 - Calculus II-Stewart Dr. Berg Spring...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online