Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The constant $a$ is defined by $\int_1^a 6x\ln x\,dx = 4.$
(a)[5]
Show that $a = \exp\left(\frac{1}{6}\left(\frac{5}{a^2} + 3\right)\right)$, where $\exp(x)$ means $e^x$.
(b)[2]
Check by calculation that $a$ lies between $2$ and $2.1$.
(c)[3]
Use an iterative formula taken from the equation in part (a) to find $a$ correct to $2$ decimal places. State 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: “Begin the integration and arrive at $\int(px^2\ln x+q)x\,dx$” …