Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram displays the curve $y = e^x + 4e^{-2x}$ together with its minimum point $M$.
(i)[3]

Show that the $x$-coordinate of $M$ equals $\ln 2$.

(ii)[4]

The shaded region shown in the diagram is enclosed by the curve and the lines $x = 0$, $x = \ln 2$ and $y = 0$. Use integration to show that the area of the shaded region is $\frac{5}{2}$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate to give $e^x - 8e^{-2x}$

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