Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The constant $a$ is chosen so that $\int_{0}^{a} x e^{\frac{1}{2}x}\,dx = 6$.
(a)[5]
Show that this gives $a = 2 + e^{-\frac{1}{2}a}$.
(b)[2]
Verify by computation that $a$ is between $2.2$ and $2.4$.
(c)[3]
Use an iterative formula based on the equation in part (a) to find $a$ correct to $2$ decimal places. State the outcome of each iteration 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: “Use integration by parts to evaluate the integral.” …