Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
We are told that $\int_0^a x\cos x\,dx = 0.5$, with $0 < a < \frac{1}{2}\pi$.
(i)[4]
Hence demonstrate that $a$ satisfies $\sin a = \frac{1.5 - \cos a}{a}$.
(ii)[2]
Confirm by calculation that $a$ is greater than $1$.
(iii)[3]
Apply the iterative formula $a_{n+1} = \sin^{-1}\left(\frac{1.5 - \cos a_n}{a_n}\right)$ to find $a$ correct to $4$ decimal places, giving each iteration to $6$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carry out the integration and arrive at $x\sin x+\int\sin x\,dx$” …