Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are told that $\int_0^a (3e^{2x} - 1)\,dx = 12$, with $a$ a positive constant.
(a)[4]
Show that the value of $a$ satisfies $a = \frac{1}{2} \ln\left(9 + \frac{2}{3}a\right)$.
(b)[3]
Use an iterative formula built from the equation in part (a) to determine the value of $a$ correct to 4 significant figures. Start with the initial value $1$ and give the result of each iteration to 6 significant figures.
Worked solution & mark scheme
This 7-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 $k_1 e^{2x}+k_2 x$” …