Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram illustrates the curve $y = 3e^{2x-1}$. The shaded region is enclosed by the curve and the lines $x = a$, $x = a + 1$ and $y = 0$, with $a$ a constant. The area of the shaded region is stated to be $120$ square units.
(a)[5]
Show, from the working, that $a = \frac{1}{2}\ln(80 + e^{2a-1}) - \frac{1}{2}$.
(b)[3]
Use the iteration process based on the equation in part (a) to determine the value of $a$ correct to $3$ significant figures. Record the outcome 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 in the form $k e^{2x-1}$” …