This page gives you the key ideas to recognise before you start a question. The full course then takes you through the method, exam-style practice and fully worked solutions.
Reverse the power rule
Increase the power by 1 and divide by the new power, treating each term separately.
Include the constant
For indefinite integration, include + C because differentiating any constant gives zero.
Use limits carefully
For a definite integral, find the antiderivative first, then evaluate upper limit minus lower limit.
Interpret area
A definite integral gives signed area. Parts below the x-axis contribute negatively, so geometric area may need separate treatment.
Worked example: indefinite integration
∫(6x² − 4x) dx
= 2x³ − 2x² + C
= 2x³ − 2x² + C
Common mistakes to avoid
- Forgetting + C on an indefinite integral.
- Dividing by the old power rather than the new power.
- Assuming a definite integral is always the same as total geometric area.