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CAIE A Level Mathematics 9709

Integration (A2) questions

Exam-style questions on Integration (A2), ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationEvaluate ∫0^3 (4x + 1) dx.
  2. 2 marksStandardFind ∫ sin(4x + 4) dx.
  3. 4 marksStandardUse the substitution u = x^2 + 1 to evaluate the definite integral ∫0^4 x(x^2+1) dx
  4. 2 marksStandardFind ∫ (2x + 1)^3 dx.
  5. 2 marksStandardEvaluate ∫0 4x^3 dx.
  6. 4 marksStandardUse the substitution u = 3x + 1 to evaluate the definite integral ∫0^2 (3x + 1)^3 dx giving your answer exactly.
  7. 2 marksStandardFind ∫ sec^2(6x + 2) dx.
  8. 2 marksStandardFind ∫ cos(6x) dx.
  9. 2 marksStandardFind ∫ e^8x + 4 dx.
  10. 2 marksStandardFind ∫ (1)/(7x - 2) dx.
  11. 2 marksStandardEvaluate ∫0^2 6x^2 dx.
  12. 3 marksChallengeFind ∫ (10x)/(x^2 + 1) dx.
  13. 5 marksChallengeUse integration by parts to evaluate the definite integral: ∫0^(π)/(4) x sin(2x) dx Give your answer as a simplified fraction.