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Course: MAT421 Calculus I

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QUESTION 5 a) Set up the integrals (with respect to x) to represent the total area of the shaded region bounded by the curves y = x2.y = 2x+3 and 3/ =4 _ (DO NOT SOLVE THE INTEGRALS) (4 marks) b) Consider the shaded region which is bounded by the curves x = y +2 and x =4-y as shown below. x =y+2 X X =4- y2 i) Show that the intersection points of both curves are (3,1) and (0,-2). (3 marks) ii) Using Washer method, find the volume of a solid obtained by revolving the shaded region about the line x =4. (5 marks) ii) Using Shell method, find the volume of a solid obtained by revolving the shaded region about the line y = 1