Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
It is stated that $\int_0^a \left(\frac{1}{2}e^{3x} + x^2\right)\,dx = 10$, where $a$ is a positive constant.
(i)[4]
Show that, after rearrangement, $a = \frac{1}{3}\ln(61 - 2a^3)$.
(ii)[2]
Show by calculation that the value of $a$ lies between $1.0$ and $1.5$.
(iii)[3]
Using an iterative formula derived from the equation in part (i), determine the value of $a$ correct to $3$ decimal places. State each iterative value to $5$ 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 to get $ke^{3x}+mx^3$” …