CAIE A-Level Mathematics 1.8.1 Basic Integration

CAIE A-Level Mathematics 1.8.1 Basic Integration
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise rewriting integrands with identities or algebra before reversing the power or chain rule to integrate constants, sums, rational powers and composite linear forms.

How this is tested

  • rewrite products, fractions or trig squares as a sum of standard integrable terms
  • increase each power by one and divide by its new exponent, retaining coefficients
  • recognise a composite linear argument and divide by its inner derivative after integration

Question 2(b)

[Maximum number: 3]

Let f(x)=4sin⁡23x\mathrm{f}(x)=4 \sin ^{2} 3 x.

Find ∫f(x)dx\int \mathrm{f}(x) \mathrm{d} x.