Created by T Madas Question 42 (****) y y = 3x − B O R P x y = x − x2 A The figure above shows the graph of the curve C with equation y = x − x2 , x ∈ » , intersected by the straight line L with equation y = 3x − , x ∈ » As shown in the above figure, C meets L at the points A and B , and crosses the x axis at the origin O and at the point P The finite region R is bounded by C , L and the x axis Show that the area of R , shown shaded in the figure, is 19 proof Created by T Madas Created by T Madas Question 43 (****) y A M y = x(6 − x) O x The figure above shows the curve C with equation y = x (6 − x) , x ∈ » The point M is the maximum point of C and the point A has coordinates ( 0,12 ) Find the exact area of the shaded region, bounded by the curve, the y axis and the straight line segment from A to M area = 27 Created by T Madas Created by T Madas Question 44 (****) y M y = 8x − x2 O A x The figure above shows the quadratic curve with equation y = 8x − x2 , x ∈ » The point M is the maximum point of the curve and the point A is one of the curve’s x intercepts Find the exact area of the shaded region, bounded by the curve, the x axis and the straight line segment from A to M area = 224 Created by T Madas