Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
We are told that $\int_{1}^{a} \ln(2x)\,dx = 1$, with $a > 1$.
(i)[6]
Show that $a = \frac{1}{2}\exp\left(1 + \frac{\ln 2}{a}\right)$, where $\exp(x)$ stands for $e^x$.
(ii)[3]
Apply the iterative formula $a_{n+1} = \frac{1}{2}\exp\left(1 + \frac{\ln 2}{a_n}\right)$ to find the value of $a$ correct to 2 decimal places. Record each iteration to 4 decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carry out the integration and obtain $x\ln 2x-\int \frac{x}{x}\,dx$, or an equivalent form” …