CAIE A-Level Mathematics 3.5.1 Extended Integration Rules

CAIE A-Level Mathematics 3.5.1 Extended Integration Rules
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise integrating exponential, trigonometric, reciprocal-linear and inverse-tangent forms by reverse differentiation and evaluating exact definite integrals or shaded areas.

How this is tested

  • integrate exponential or trig functions of ax + b with the reciprocal inner factor
  • recognise 1/(a² + x²) as an inverse-tangent form and retain its scale factor
  • apply exact bounds and combine curve, rectangle or triangle areas with the correct sign

Question 4

[Maximum number: 5]

Given that ∫aa+1413x dx=ln⁡2\int_{a}^{a+14} \frac{1}{3 x} \mathrm{~d} x=\ln 2, find the value of the positive constant a.