Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The condition is $\int_0^a (3x^2 + 4\cos 2x - \sin x)\,dx = 2$, with $a$ taken as a constant.
(i)[4]
Show that $a$ satisfies $a = \sqrt[3]{(3 - 2\sin 2a - \cos a)}$.
(ii)[2]
Use the equation from part (i) and calculate to show that $0.5 \le a \le 0.75$.
(iii)[3]
Apply an iterative formula, based on the equation in part (i), to determine $a$ correct to 3 significant figures. Record each iteration to 5 significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrate to reach an expression of the form $x^3 + k_1 \\sin 2x + k_2 \\cos x$” …