CAIE A-Level Mathematics 2.5.2 Trig integration

CAIE A-Level Mathematics 2.5.2 Trig integration
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using trig relationships to rewrite integrands, integrate powers of sin and cos, and evaluate exact definite integrals.

How this is tested

  • rewrite sin^2 x or cos^2(2x) using double-angle formulae before integrating
  • apply exact limits involving π to obtain values with radicals, fractions or π terms

Question 6

[Maximum number: 7]

Show that ∫14π13π(4cos⁡22x+1cos⁡2x)dx=343+16π−1\int_{\frac{1}{4} \pi}^{\frac{1}{3} \pi}\left(4 \cos ^{2} 2 x+\frac{1}{\cos ^{2} x}\right) d x=\frac{3}{4} \sqrt{3}+\frac{1}{6} \pi-1.