4.
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The diagram shows the curve with equation \(y = \frac { 1 } { x ^ { 2 } + 1 }\).
The shaded region \(R\) is bounded by the curve, the coordinate axes and the line \(x = 2\).
- Use the trapezium rule with four strips of equal width to estimate the area of \(R\).
The cross-section of a support for a bookshelf is modelled by \(R\) with 1 unit on each axis representing 8 cm . Given that the support is 2 cm thick,
- find an estimate for the volume of the support.