Study notes

Integration

Integration as the reverse of differentiation for polynomials, always with '+C' on indefinite integrals, definite integrals, area under a curve, and simple kinematics.

What this topic covers

  • Integration reverses the power rule: raise the power by one, then divide by the NEW power
  • An indefinite integral must ALWAYS end in '+C'; forgetting it is a real, common error
  • A constant on its own integrates to (constant) \(\times\, x\), plus C
  • A definite integral has limits and gives a NUMBER, with no '+C'
  • The area under a curve, above the x-axis, between two x-values is a definite integral
  • Kinematics: displacement, velocity, and acceleration are linked by differentiation and integration in opposite directions

Read the full Integration notes, free

Sign up free (100% free, no credit card) to unlock the full study notes, worked examples and mind map, and save your child's progress across devices.

Already have an account? Sign in

Practise this topic →