Integration undoes differentiation, and then does something differentiation can't: it measures area. The two halves of the topic are the technique and knowing which area the question actually wants.
Syllabus points covered
- Integrate xⁿ, eᵃˣ⁺ᵇ, sin(ax + b), cos(ax + b) and 1/(ax + b)
- Evaluate definite integrals and use them to find areas under and between curves
- Find a function from its derivative given a point on the curve
- Apply integration to kinematics problems
Common mistakes
- Forgetting the constant of integration on an indefinite integral, and forgetting to find it when a point is given.
- Missing the 1/a factor when integrating a function of (ax + b).
- Subtracting the limits the wrong way round in a definite integral.
- Treating a region that crosses the x-axis as one integral — split it, or the positive and negative areas cancel.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers