7B_2016-2017_H2_Maths_App_of_Integration_Assignment_2

National Junior College Mathematics Department 2015 Applications of Integration (Area and Volume) Page 1 of 1 National Junior College 2016 – 2017 H2 Mathematics Applications of Integration (Area and Volume) Assignment 2 Name: _____________________________ Class: 1ma2__ / 1IPma21__ / 1IPma22__ Subject Tutor: _________________ You are advised to use only MF26, and complete this assignment in one sitting. 1 The region A is bounded by the curve 2 1 xy and the lines 4,  yxy and 0x . (i) Find the area of region A. [3] (ii) Find the exact volume formed when region A is rotated through 2π radians about the y-axis. [4] 2 The region R is bounded by the axes and the part of the curve 2 4 ( ), 0,y a a x a   lying in the first quadrant. Find, in terms of a, (i) the area of R, [3] (ii) the volume, ,xV of the solid formed when R is rotated completely about the x-axis. [3] The volume of the solid formed when R is rotated completely about the y-axis is yV . (iii) Show that xy VV 15 8 . [3] The region S, lying in the first quadrant, is bounded by the curve )(42 xaay  and the lines ax and ay 2 . Find, in terms of a, the volume of the solid formed when S is rotated completely about the y-axis. [2] 3 A curve has parametric equations 1 2sinx  , cosy  , where .22     (i) Sketch the curve, labelling clearly any intercepts with the axes. [3] (ii) Find the exact area of the region bounded by the curve, the line 2x , and both the x- and y- axes. [4] Suggested Duration: 40min Time Spent: Commented [BACA1]: Change the year here and in header Commented [BACA2]: Non italic pi