Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are told that $\int_0^a (3e^{3x} + 5e^x)\,dx = 100$, with $a$ a positive constant.
(i)[5]
Show that $a = \frac{1}{3}\ln(106 - 5e^a)$ as required.
(ii)[3]
Use an iterative formula based on the equation in part (i) to determine the value of $a$ correct to $3$ decimal places. Record the outcome of each iteration to $5$ decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrate and obtain $e^{3x}+5e^x$.” …