Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

It is stated that $a$ is a positive constant for which $\int_0^a (1 + 2x + 3e^{3x})\,dx = 250$.
(i)[5]

Show that the equation can be rearranged to give $a = \tfrac{1}{3}\ln(251 - a - a^2)$.

(ii)[3]

Use an iterative formula derived from the equation in part (i) to determine $a$ correct to 4 significant figures. State the value from every iteration to 6 significant figures.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Integrate to obtain the form $k_1x+k_2x^2+k_3e^{3x}$ for non-zero constants

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI