(a)[3]
Determine the gradient of the curve at $A$.
(b)[5]
Show that the $x$-coordinate of $B$ is $\ln 2$ and then find the area of the shaded region.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
The diagram depicts the curve with equation $y = 8\mathrm{e}^{-x} - \mathrm{e}^{2x}$. This curve meets the $y$-axis at $A$ and the $x$-axis at $B$. The shaded area lies between the curve and the two coordinate axes.