Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
Given that $\int_1^a \left( \frac{4}{1+2x} + \frac{3}{x} \right)\, dx = \ln 10$, where $a$ is a constant greater than $1$.
(a)[5]
Hence show that $a = \sqrt[3]{90(1+2a)^{-2}}$.
(b)[3]
Use an iterative formula, based on the equation in part (a), to determine the value of $a$ correct to $3$ significant figures. Take an initial value of $1.7$ and give each iteration result 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: “Carry out the integration to obtain an expression of the form $k_1\ln(1+2x)+k_2\ln x$, with $k_1\neq0$, $k_2\neq0$” …