Pure · Integration
Chapter 1 · 4
The idea
The constant of integration
Why every indefinite integral carries a "+C", what that constant actually represents, and how extra information (a point on the curve, an initial condition) pins it down.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Integration
The constant of integration
Why every indefinite integral carries a "+C", what that constant actually represents, and how extra information (a point on the curve, an initial condition) pins it down.
Why it works
Differentiation destroys information
The functions , and all have exactly the same derivative, — differentiating wipes out any constant term, because a constant changes nothing about the slope of a graph.A family of curves
Integration is the reverse of differentiation. So when you ask "what function has derivative ?", the honest answer is: a whole family of functions — for any constant . You cannot know which member of the family is "the" answer from the derivative alone, because the derivative never contained that information in the first place.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
Start freeTakes a minute — no card.