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\includegraphics[max width=\textwidth, alt={}, center]{567c3d72-c633-4ae0-8605-f63f93d718c4-18_979_679_262_731}
The diagram shows part of the curve \(y = 1 - \frac { 4 } { ( 2 x + 1 ) ^ { 2 } }\). The curve intersects the \(x\)-axis at \(A\). The normal to the curve at \(A\) intersects the \(y\)-axis at \(B\).
- Obtain expressions for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\int y \mathrm {~d} x\).
- Find the coordinates of \(B\).
- Find, showing all necessary working, the area of the shaded region.
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