Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The information provided is that $\int_0^a (1 + e^{\frac{1}{2}x})^2\,dx = 10$, with $a$ a positive constant.
(i)[6]
Hence, show that $a = 2\ln\left(\frac{15 - a}{4 + e^{\frac{1}{2}a}}\right)$.
(ii)[2]
Using the equation from part (i), show by calculation that $1.5 \le a \le 1.6$.
(iii)[3]
Use an iterative formula derived from the equation in part (i) to determine the value of $a$ correct to 3 significant figures. Present 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 $1+2e^{\frac{1}{2}x}+e^x$” …