Integrating Powers of x (Edexcel IAL Maths)

Spec point — 5.2

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

Spec point — 5.1

How do I find the constant of integration?

• 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

Worked Example