When integrating, why do we add a constant to the resulting equation?

The +c is to represent the loss in information after differentiation. Remember, integration is just the reverse of differentiation. Say we had this function:

f(x) = 2x^2 + 1 And we differentiate: f'(x) = 4x

Now take this second function: g(x) = 2x^2 + 4 And differentiating gives us: g'(x) = 4x

We can see that g'(x) = f'(x). So, if we try and integrate 4x, what do we get? Would it be 2x^2 + 1, or 2x^2 + 4?

The answer is it could be either. Or 2x^2 + 3. Or 2x^2 + 109823.1203981! There are infinite solutions to integration, depending on how you got there from differentiating. That's why we add the +c - to represent all the different possibilities.

TC
Answered by Tom C. Maths tutor

3698 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

When trying to solve inequalities (e.g. 1/(x+2)>x/(x-3)) I keep getting the wrong solutions even though my algebra is correct.


Find the exact gradient of the curve y=ln(1-cos2x) at the point with x-coordinate π/6


How do I use the chain rule to differentiate polynomial powers of e?


Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences