Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are told that $\int_0^p 4x e^{-\frac{1}{2}x} \, dx = 9$, with $p$ being a positive constant.
(i)[5]
Show, therefore, that $p = 2\ln\left(\frac{8p + 16}{7}\right)$.
(ii)[3]
Use an iterative method based on the equation in part (i) to determine the value of $p$ correct to $3$ significant figures. Take $3.5$ as the starting value and record each iteration 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: “Using integration by parts, derive $axe^{-x/2}+\int be^{-x/2}dx$” …