Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are given that $\int_{0}^{a} (1 + e^{\frac{1}{2}x})^{2} \, dx = 10$, where $a$ is a positive constant.
(i)[6]
Show that $a = 2\ln\left(\dfrac{15 - a}{4 + e^{\frac{1}{2}a}}\right)$.
(ii)[2]
Use the equation in part (i) to show by calculation that $1.5 \le a \le 1.6$.
(iii)[3]
Use an iterative formula based on the equation in part (i) to find the value of $a$ correct to $3$ significant figures. Record the outcome of each iteration to $5$ significant figures.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Express the integrand as $1+2e^{x/2}+e^x$” …