The diagram shows part of the curve $y= \mathrm{e}^{x-1}-2$. The point $P(2, e-2)$ lies on the c

Question

The diagram shows part of the curve $y= \mathrm{e}^{x-1}-2$. The point $P(2, e-2)$ lies on the curve and the normal to the curve at $P$ meets the $x$-axis at $Q$. Find the $x$-coordinate of $Q$ in terms of $\mathrm{e}$.[5] Find the total area under the shaded region.[7]

Accepted Answer

(a) $x_Q=e(e-2)+2$ (b) $2.56\text{ units}^2$

2025 CGSS PRELIMS P2 Q10

2025 CGSS PRELIMS P2 Q10

Solution:

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