Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
We are told that $\int_0^a \left( \frac{4}{2x + 1} + 8x \right) \, dx = 10$, where $a$ is a positive constant.
(a)[4]
Show that this gives $a = \sqrt{2.5 - 0.5 \ln(2a + 1)}$.
(b)[2]
Using the equation from part (a), show by calculation that $1 \le a \le 2$.
(c)[3]
Use an iterative formula based on the equation in part (a) to determine the value of $a$ correct to $4$ significant figures. State each iterate to $6$ significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrate to get $k_1\ln(2x+1) + k_2x^2$” …