Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The figure displays the curve $y = 3e^{2x-1}$. The shaded area is enclosed by the curve together with the lines $x = a$, $x = a + 1$ and $y = 0$, where $a$ is a constant. The area of this shaded region is given as $120$ square units.
(a)[5]
Show, by manipulation, that $a = \frac{1}{2}\ln(80 + e^{2a-1}) - \frac{1}{2}$.
(b)[3]
Use an iterative formula, taken from the equation in part (a), to determine the value of $a$ correct to $3$ significant figures. Record the result of every iteration to $5$ significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrate so that the result is written in the form $ke^{2x-1}$” …