Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram presents the curve with equation $y=\frac{x-2}{x^2+8}$. The shaded area is enclosed by the curve together with the lines $x=14$ and $y=0$.
(a)[4]

Find $\frac{dy}{dx}$ and then determine the exact $x$-coordinates of the stationary points.

(b)[3]

Use the trapezium rule with three intervals to estimate the area of the shaded region. Give your answer correct to $2$ significant figures.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate by using the quotient rule (or product rule)

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