Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The constant $a$ is defined by $\int_{0}^{a} x e^{-2x}\, dx = \frac{1}{8}$.
(a)[5]
Demonstrate that $a = \frac{1}{2} \ln(4a + 2)$.
(b)[2]
Confirm by calculation that $a$ lies between $0.5$ and $1$.
(c)[3]
Apply the iterative formula arising from the equation in (a) to find $a$ correct to 2 decimal places. Record every iterate to 4 decimal places.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Begin the integration properly and reach $pxe^{-2x}+q\int e^{-2x}\,dx$.” …