Area Using Substitution or Rearrangement

Find area by first making a substitution (e.g., u = 2x - 3) or rearranging to integrate with respect to y instead of x.

1 questions · Standard +0.3

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CAIE P1 2023 November Q8
9 marks Standard +0.3
8 \includegraphics[max width=\textwidth, alt={}, center]{5e3e5418-7976-4232-8550-1da6420a3fcb-12_684_776_274_680} The diagram shows the curves with equations \(y = 2 ( 2 x - 3 ) ^ { 4 }\) and \(y = ( 2 x - 3 ) ^ { 2 } + 1\) meeting at points \(A\) and \(B\).
  1. By using the substitution \(u = 2 x - 3\) find, by calculation, the coordinates of \(A\) and \(B\).
  2. Find the exact area of the shaded region.