CAIE A-Level Mathematics 2.5.1 Extended Integration Rules

CAIE A-Level Mathematics 2.5.1 Extended Integration Rules
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise integrating exponential, reciprocal-linear and trigonometric forms by reverse differentiation, retaining scale factors and evaluating exact definite integrals or areas.

How this is tested

  • integrate e^(ax+b) by dividing by a and integrate 1/(ax+b) as (1/a)ln|ax+b|
  • integrate sin, cos or sec² of a linear argument with the correct reciprocal scale factor
  • apply exact bounds and use logarithm laws or intersections to simplify the final value or area

Question 4(b)

Figure for Question 4(b) — CAIE A-Level Mathematics

The diagram shows the curve with equation y=6e2x−e3xy=6 \mathrm{e}^{2 x}-\mathrm{e}^{3 x}. The shaded region is bounded by the axes and the curve.

Find the area of the shaded region. Give your answer in the form pq\frac{p}{q}, where p and q are integers.