Finding the Constant of Integration (DP IB Analysis & Approaches (AA)): Revision Note

Finding the Constant of Integration

What is the constant of integration? 

• When finding an anti-derivative there is a constant term to consider

  • this constant term, usually called , is the constant of integration

• In terms of graphing an anti-derivative, there are endless possibilities

  • collectively these may be referred to as the family of antiderivatives or family of curves

  • the constant of integration is determined by the exact location of the curve

    • if a point on the curve is known, the constant of integration can be found

How do I find the constant of integration?

• For , the constant of integration,  - and so the particular antiderivative - can be found if a point the graph of  passes through is known 

 STEP 1

 If need be, rewrite into an integrable form

 Each term needs to be a power of  (or a constant)

 STEP 2

 Integrate each term of, remembering the constant of integration, “”

 (Increase power by 1 and divide by new power)

 STEP 3

Substitute the  and  coordinates of a given point in to  to form an equation in 

Solve the equation to find