Edexcel F3 2024 January — Question 1

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2024
SessionJanuary
TopicIntegration using inverse trig and hyperbolic functions

  1. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
  1. Show that $$\int _ { 4 } ^ { 4 \sqrt { 3 } } \frac { 8 } { 16 + x ^ { 2 } } d x = p \pi$$ where \(p\) is a rational number to be determined.
  2. Determine the exact value of \(k\) for which $$\int _ { \frac { 3 } { 4 } } ^ { k } \frac { 2 } { \sqrt { 9 - 4 x ^ { 2 } } } d x = \frac { \pi } { 12 }$$