Finding the Constant of Integration (DP IB Applications & Interpretation (AI)): 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

    • They all have the same shape, but are just shifted up or down vertically compared to each other

    • Each one corresponds to a different possible value of

• The value of 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, , can be found if a point on the graph of  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 “”

    

• STEP 3

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

  Solve the equation to find