Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are given that $\int_1^a \ln(2x)\,dx = 1$, with $a > 1$.
(i)[6]
Show that $a = \frac{1}{2}\exp\left(1 + \frac{\ln 2}{a}\right)$, with $\exp(x)$ representing $e^x$.
(ii)[3]
Use the iterative formula $a_{n+1} = \frac{1}{2}\exp\left(1 + \frac{\ln 2}{a_n}\right)$ to find $a$ correct to $2$ decimal places, and 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: “Integrate to obtain $b x\ln2x-c\int\frac{1}{x}\,dx$, or an equivalent expression” …