Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram illustrates the section of the curve $y = \sqrt{(2 - \sin x)}$ for $0 \le x \le \frac{1}{2}\pi$.
(i)[3]
Use the trapezium rule with 2 intervals to estimate the value of $\int_0^{\frac{1}{2}\pi} \sqrt{(2 - \sin x)} \, dx$, and give your answer correct to 2 decimal places.
(ii)[3]
The line $y = x$ crosses the curve $y = \sqrt{(2 - \sin x)}$ at the point $P$. Apply the iterative formula $x_{n+1} = \sqrt{(2 - \sin x_n)}$ to find the $x$-coordinate of $P$ correct to 2 decimal places. Show the result of each iteration to 4 decimal places.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or indicate the correct ordinates $1.4142\ldots$, $1.1370\ldots$, $1$” …