am i) Find an equation of the tangent to the curve at the point A. [2 marks] ii) Find coordinates of point B. [1 mark] iii) The curve crosses the x-axis at the point C. Calculate the area of the shaded region bounded by the tangent, curve and x-axis. [4 marks] b) Integrate with respect to x I exVZ + ex dx [3 marks] 7. a) The area enclosed between the curves y = x2 and y2 = x is rotated about the x-axis. Find the volume generated. [5 marks] b) Obtain the general solution of the differential equation \\llxzdyx 1y2dx = 0 [5 marks] 4 of 7 6. a) The figure below shows a curve and the tangent to the curve at point A. The curve has equation y = 3x3 + x2 4x + 12 and the point A(1,14) lies on the curve. The tangent at A crosses the x-axis at point B. i) Find an equation of the tangent to the curve at the point A. [2 marks] in Bind nnnrdirm \f