Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram depicts the curves $y = e^{2x}$ and $y = 8e^{-x}$, with the shaded area enclosed by both curves and the $y$-axis.
(a)[2]

Show that the $x$-coordinate of the intersection of the two curves is $\ln 2$.

(b)[3]

Find the area enclosed by the shaded region.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: State $e^{2x}=8e^{-x}$ and derive $3x=\ln 8$ or $e^x=2$

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