2.
\section*{In this question you must show all stages of your working.}
\section*{Solutions relying entirely on calculator technology are not acceptable.}
- Express as an integral
$$\lim _ { \delta x \rightarrow 0 } \sum _ { x = 4 } ^ { 12 } ( 1 + 2 x ) ^ { \frac { 1 } { 2 } } \delta x$$
- Using your answer to part (a) show that
$$\lim _ { \delta x \rightarrow 0 } \sum _ { x = 4 } ^ { 12 } ( 1 + 2 x ) ^ { \frac { 1 } { 2 } } \delta x = \frac { 98 } { 3 }$$
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