CAIE A-Level Mathematics 3.5.5 Inverse tangent

CAIE A-Level Mathematics 3.5.5 Inverse tangent
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise integration by parts for products involving x, x^2, exponentials, ln x and tan^-1 expressions, including exact areas.

How this is tested

  • reduce the remaining integral after parts to a standard ln, tan^-1 or exponential form
  • use integration by parts inside area calculations with given bounds and exact answers

Question 10(b)

[Maximum number: 6]

Find the exact value of ∫00.5xtan⁡−1(2x)dx\int_{0}^{0.5} x \tan ^{-1}(2 x) \mathrm{d} x.