The diagram shows the curve $y = \surd \left( {1 + {x^3}} \right)$. 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 $y = 3$.
a) 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.
b) Deduce an approximation to the area of region $B$ and explain why this approximation under estimates the true area of region $B$.

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