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Figure $1$ Figure $1$ shows part of the curve with equation $y = e^{\frac{1}{3^2}}$ for $x \geq 0$ The finite region $R$, shown shaded in Figure $1$, is bounded by the curve, the $y$-axis, the $x$-axis, and the line with equation $x = 2$ The table below shows corresponding values of $x$ and $y$ for $y = e^{\frac{1}{x^2}}$$\newline$$x$$\newline$$0$$\newline$$0$.$5$$\newline$$1$$\newline$$1$.$5$$\newline$$2$$\newline$$y$$\newline$$1$$\newline$$x \geq 0$$1$$\newline$$x \geq 0$$2$$\newline$$x \geq 0$$3$$\newline$$x \geq 0$$4$$\newline$(a) Use the trapezium rule, with all the values of $y$ in the table, to find an estimate for the area of $R$, giving your answer to $2$ decimal places. ($3$) (b) Use your answer to part (a) to deduce an estimate for (i) $x \geq 0$$7$ (ii) $x \geq 0$$8$ giving your answers to $2$ decimal places. a)