(a)[3]
Find the gradient at $A$ on the curve.
(b)[5]
Show that the $x$-coordinate of $B$ is $\ln 2$ and hence determine the area of the shaded region.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram depicts the curve with equation $y = 8e^{-x} - e^{2x}$. The curve meets the y-axis at point $A$ and the x-axis at point $B$. The shaded area is enclosed by the curve and the two axes.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to give an expression of the form $k_1 e^{-x}+k_2 e^{2x}$” …
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