Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The constant $a$ is defined so that $\int_{1}^{a} \frac{\ln x}{\sqrt{x}}\,dx = 6$.
(a)[5]
Show that $a = \exp\left(\frac{1}{\sqrt{a}} + 2\right)$. [Note: $\exp(x)$ is an alternative way to write $e^x$.]
(b)[2]
Verify by calculation that $a$ lies between $9$ and $11$.
(c)[3]
Use an iterative formula based on the equation in part (a) to determine $a$ correct to $2$ decimal places. Give the result of 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: “Commence integration and arrive at $a\sqrt{x}\ln x+b\sqrt{x}\cdot \frac{1}{x}\,dx$ or an equivalent form” …