Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

Paper 3, Section I, B

Further Complex Methods | Part II, 2018

Using a suitable branch cut, show that

∫−aa(a2−x2)1/2dx=a2π2,\int_{-a}^{a}\left(a^{2}-x^{2}\right)^{1 / 2} d x=\frac{a^{2} \pi}{2},∫−aa​(a2−x2)1/2dx=2a2π​,

where a>0a>0a>0.

Typos? Please submit corrections to this page on GitHub.