Constants of Integration (Edexcel IGCSE Further Pure Maths)

Finding the Constant of Integration

What is the constant of integration? 

• The constant of integration is the used when finding an indefinite integral 

  • e.g.

  • can be any constant

• Integration and differentiation are inverse operations

  • That means if you differentiate your answer to an integral...

    • ...it should turn back into the original function you integrated

  • The 'problem' is that the derivative of a constant is zero

    • 

    • 

    • 

  • So  plus or minus any constant is a valid solution to 

• But consider the graph of

  • Different values of  represent different vertical translations of the graph

  • If we know one point on that graph we can work out the value of 

How do I find the constant of integration?

• On an exam you may be given a derivative or

  • You can integrate that to find  or  in '' form

    • 

    • 

• If you are also given a point on the graph of  or of 

  • you can use this to find the value of 

  • Substitute the values you know into or

    • Then solve for

• The extra information doesn't have to be a point on a graph

  • As long as you know the value of for one value of 

    • you can substitute and solve to find