help me to show the working with correct answer

SET 1 QUESTION 3 QUESTION 1 The function h is defined as h(x) = 4_,7. x51 A region R bounded by the curves y = 3x -6 and y =-3x. x' Inx, x > I Show that [ h(x ) dx = 4In2 - 15 (a) Sketch the curves on the same axes and shade the region R. [3 marks] (C3, CLO3, MQF LOD 6) [7 marks] Matrikiki Lobby (C3, CLO3, MOF LOD 6) (b) Find the intersection points between these two curves. [2 marks] (C3, CLO3, MQF LOD 6) QUESTION 2 (c) Calculate the area of the region R. [4 marks] (C3, CLO3, MQF LOD 6) (a) Find the integral of dx . Provide your final answer as a single logarithm. KMJ [6 marks] Kellemean Menjana (C3, CLO3, MQF LOD 6) (d) Calculate the volume of the solid generated when the shaded region is rotated through radians about the y-axis terrance PAEan [5 marks] (C3, CLO3, MQF LOD 6) (b) Show that dr = Lan Zx + c [4 marks] (C3, CLO3, MQF LOD 6) QUESTION 4 By using integrating factor, solve the following differential equation -2x2y + x3 9%- xef = 0, y(1) = e. [9 marks] (C3, CLO3, MQF LOD 6)