The points $A$ and $B$ lie on the curve $y=2\mathrm{e}^{-x}+1$, where their $x$-coordinates

Question

The points $A$ and $B$ lie on the curve $y=2\mathrm{e}^{-x}+1$, where their $x$-coordinates are $0$ and $2$, respectively. The chord $AB$ is drawn. State the coordinates of $A$ and $B$.[2] Find the exact area enclosed by the curve and the chord $AB$.[5]

Accepted Answer

(i) $A=(0,3)$, $B=(2,1+2\mathrm e^{-2})$ (ii) $4\mathrm e^{-2}\text{ units}^2$

Exponential curve and a chord

Exponential curve and a chord

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