SPS SPS FM Pure 2023 June — Question 15

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2023
SessionJune
TopicStandard Integrals and Reverse Chain Rule

15. In this question you must use detailed reasoning.
  1. Show that \(\int _ { \frac { \pi } { 3 } } ^ { \frac { \pi } { 2 } } \frac { 1 + \sin 2 x } { - \cos 2 x } d x = \ln ( \sqrt { a } + b )\), where \(a\) and \(b\) are integers to be determined.
  2. Show that \(\frac { \pi } { \frac { \pi } { 4 } } \frac { 1 + \sin 2 x } { - \cos 2 x } d x\) is undefined, explaining your reasoning clearly.
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