My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
October 19th, 2017, 08:44 PM   #1
Joined: Jan 2014

Posts: 19
Thanks: 0

Notation for indefinite integrals

The notation $\int{f(x)}\,dx$ is commonly used to denote the set of ALL antiderivatives of the function $f$. My question: Is it wrong to use the notation $\int{f(x)}\,dx$ to denote a single antiderivative of the function $f$ without the constant of integration $c$?

I saw many instances where the notation $\int{f(x)}\,dx$ is use to denote a single antiderivative with the constant of integration omitted. For example to evaluate $\int {xe^x}\,dx$, some textbooks wrote $v=\int\,dv=\int{e^x}\,dt=e^x$, without the constant of integration. For example, to solve the differential equation $y'+\frac{2}{t}y=e^t$ by using an integrating factor, some textbooks wrote $\mu(t)=\exp(\int{2/t}\,dt)=t^2$, without a constant of integration.
woo is offline  
October 19th, 2017, 11:03 PM   #2
Senior Member
Joined: Feb 2016
From: Australia

Posts: 1,801
Thanks: 636

Math Focus: Yet to find out.
Try introducing a constant at that step. You will end up with a sum of multiple of arbitrary constants which is still arbitrary, and we simply 'recycle' them.
Joppy is offline  
October 20th, 2017, 02:21 AM   #3
Global Moderator
Joined: Dec 2006

Posts: 20,629
Thanks: 2077

If the integrating factor is found as the exponential function of an antiderivative, omitting the arbitrary constant doesn't matter, as a valid integrating factor results, regardless of the value of the constant.
skipjack is offline  

  My Math Forum > College Math Forum > Calculus

indefinite, integrals, notation

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
indefinite integrals notation slickidE Calculus 8 January 24th, 2017 08:10 AM
indefinite integrals Heras Calculus 2 February 13th, 2012 11:19 AM
indefinite integrals ab.empire Calculus 6 April 15th, 2009 05:03 AM
indefinite integrals ab.empire Applied Math 0 December 31st, 1969 04:00 PM
indefinite integrals Heras Real Analysis 0 December 31st, 1969 04:00 PM

Copyright © 2019 My Math Forum. All rights reserved.