Created by T Madas Question 54 (****) y y = x2 − x + P L1 R Q L2 O x The figure above shows the graph of the curve C with equation y = x2 − x + The point P is the point where C meets the y axis so that the straight line L1 is the normal to C at P a) Find an equation for L1 ( ) The point Q 3, lies on C and the straight line L2 is the normal to C at Q The finite region R , shown shaded in the figure above, is bounded by L1 , L2 and C b) Find the area of R y = x + , 15 Created by T Madas Created by T Madas Question 55 (****+) y y = x − 8x A O x R L1 L2 The figure above shows the graph of the curve C with equation y = x − 8x , x ≥ The curve meets the x axis at the origin O and at the point A The tangent to C at O is denoted by L1 and the tangent to C at A is denoted by L2 The finite region R , shown shaded in the figure above, is bounded by C , L1 and L2 Determine the area of R 384 ≈ 11.0 35 Created by T Madas Created by T Madas Question 56 (****+) y y = + x − x2 y =8 y =5 x O The figure above shows the curve C with equation y = + x − x2 , intersected by the horizontal straight lines with equations y = and y = Calculate the exact area of the shaded region, bounded by C and the two straight lines area = 28 Created by T Madas