CAIE A-Level Mathematics 1.8.3 Definite integrals

CAIE A-Level Mathematics 1.8.3 Definite integrals
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise evaluating definite integrals exactly, including logarithmic, trigonometric and improper forms with clear use of limits.

How this is tested

  • apply upper and lower limits to exact antiderivatives, including logarithmic forms
  • handle ∞ limits by showing the disappearing term before giving the exact value
  • use integration by parts or identities before evaluating a definite integral

Question 4

[Maximum number: 6]

Find the exact value of ∫01xtan⁡−1x dx\int_{0}^{1} x \tan ^{-1} x \mathrm{~d} x.