Mathematics 9709 · AS & A Level · Integration

Integration — practice question

The diagram depicts the curve $y^2 = 2x - 1$ together with the straight line $3y = 2x - 1$. These two graphs meet when $x = \frac{1}{2}$ and again when $x = a$, with $a$ being a constant.
(a(i))[2]

Show that $a = 5$ from the given conditions.

(a(ii))[6]

Find, showing all necessary working, the area of the shaded region in the diagram.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Solve $y^2=3ay$ to obtain $y=3$ or $0$

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