Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
Let $a$ be a positive constant for which $\int_0^a x e^{-\frac{1}{2}x} \, dx = 2$.
(i)[5]
Show that $a$ satisfies the equation $a = 2 \ln(a + 2)$.
(ii)[2]
Check by calculation that $a$ is between $3$ and $3.5$.
(iii)[3]
Use an iteration based on the equation in part (i) to find $a$ correct to $2$ decimal places. Write each 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: “Apply integration by parts and arrive at $I=x e^{-x/2}+m\int e^{-x/2}dx$” …