Question 5 - A-Level Maths

Find \(\int \left( x ^ { 3 } - 6 x \right) \mathrm { d } x\).
1. Find \(\int \left( \frac { 4 } { x ^ { 2 } } - 1 \right) \mathrm { d } x\).
2. The diagram shows part of the curve \(y = \frac { 4 } { x ^ { 2 } } - 1\).
  \includegraphics[max width=\textwidth, alt={}, center]{35d8bb6d-ff0f-4590-b13d-46e4869e2587-04_707_1283_708_415} The curve crosses the \(x\)-axis at \(( 2,0 )\).
  The shaded region is bounded by the curve, the \(x\)-axis, and the lines \(x = 1\) and \(x = 5\). Calculate the area of the shaded region.