OCR C3 2013 June — Question 6

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2013
SessionJune
TopicArea Under & Between Curves

6 The value of \(\int _ { 0 } ^ { 8 } \ln \left( 3 + x ^ { 2 } \right) \mathrm { d } x\) obtained by using Simpson's rule with four strips is denoted by \(A\).
  1. Find the value of \(A\) correct to 3 significant figures.
  2. Explain why an approximate value of \(\int _ { 0 } ^ { 8 } \ln \left( 9 + 6 x ^ { 2 } + x ^ { 4 } \right) \mathrm { d } x\) is \(2 A\).
  3. Explain why an approximate value of \(\int _ { 0 } ^ { 8 } \ln \left( 3 \mathrm { e } + \mathrm { e } x ^ { 2 } \right) \mathrm { d } x\) is \(A + 8\).