Integrating Powers of x (AQA A Level Maths): Revision Note

Integrating Powers of x

What is integration?

•  Integration is the inverse ('opposite') of differentiation

How do I integrate powers of x?

•  For each term …

  • … increase the power (of x) by 1

  • … divide by the new power

• This does not apply when the original power is -1

  • the new power would be 0 and division by 0 is undefined

Finding the Constant of Integration

How do I find c? 

• STEP 1  Rewrite the function into a more easily integrable form

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

• STEP 2  Integrate each term and remember “+c”

  • Increase power by 1 and divide by new power

• STEP 3  Substitute the coordinates of a given point in to form an equation in c

  • Solve the equation to find c