CAIE P2 2023 November — Question 5

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2023
SessionNovember
TopicStandard Integrals and Reverse Chain Rule

5
  1. Find the quotient when \(6 x ^ { 3 } - 5 x ^ { 2 } - 24 x - 4\) is divided by ( \(2 x + 1\) ), and show that the remainder is 6 .
  2. Hence find $$\int _ { 2 } ^ { 7 } \frac { 6 x ^ { 3 } - 5 x ^ { 2 } - 24 x - 4 } { 2 x + 1 } d x$$ giving your answer in the form \(a + \ln b\), where \(a\) and \(b\) are integers.