Question

Q2 Figure Q2 illustrates a graph that contains two parallel straight lines, with a shaded region bounded by both lines and both axes. y Line A Line B Figure Q2 (a) Find the equation of Line A and Line B respectively. (2 marks) (b) (c) Compute the area of the shaded region. (3 marks) The shaded region is revolved around y - axis. (i) Compute the volume of solid generated by revolving the bounded region between Line A and both axes around y-axis, followed by the volume of the solid generated by revolving the bounded region between Line B and both axes around the y-axis. Hence, deduce the volume of the solid generated by revolving the shaded region around y - axis. (5 marks) (ii) Compute the volume of the solid generated using Washer method. (5 marks)

Answer 1

@ Line-t. 4-0 = 1-0 (x-1) 2. yerXt1 nty A - Line-B: 2 Tx+y=2 1 © Area Area under ene-a [Area under lines) with xxy axb [Are with & ayraxis 2 Line-B : / O 2 2 1x2x2 x1x1 2 37 Lina-A: By Distrethods. v=JAlydy ALY) = HRCG), Rly)=1-4 S'or (1-yydy (Lyrik (0-1)=% By dist method Vs (Aly) dy R(Y) = 2-4 13 to (2-4) dy (12-91 (0-8) - Volume of region stepped = 817 / 2 = 1 1 1 ☺ By washer method, Vas Alydy A cy) = T[e’y) -r*149] V= 511(2-4)= (1-y%3dy + 5*r(2-43_ofy R(Y) = 2-4, fly)=sity Ww m (2.90* Cy*] + r (29), - ((1-8) – (0-1) - 1 (0-1) or + 1 = 771/3 - STT 3. 0 DYSI VEN Isus2 13