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\includegraphics[max width=\textwidth, alt={}, center]{ee420db2-bef4-4c2b-8dd2-c8f439dd561e-2_645_750_429_699}
The diagram shows the curve \(y = \sqrt { } \left( 1 + x ^ { 3 } \right)\). Region \(A\) is bounded by the curve and the lines \(x = 0\), \(x = 2\) and \(y = 0\). Region \(B\) is bounded by the curve and the lines \(x = 0\) and \(y = 3\).
- Use the trapezium rule with two intervals to find an approximation to the area of region \(A\). Give your answer correct to 2 decimal places.
- Deduce an approximation to the area of region \(B\) and explain why this approximation underestimates the true area of region \(B\).