Question

Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a = 7 and b = 2.) y-ax(x-by Sketch a typical approximating shell. y 101 ds 1.0 15 20 25 -2 1201

Answer 1

At first we draw the region bounded by the curve and linen. Then rotating the region about y axis and get a solid. Now we consider a typical shell and find out the volume of the solid using shell method.
Griven cubre Yeax sax (4-6) ? , 0= 7 and 6=2 y= 7x (2-2)~ 'Y Here shaded portion is the bounded the ion ཤུ་བར་ by the given y=an (k-b)" cure and 2 ans. →x XI 0 b Now we r rotating the region about anis and get a solid g .Y We consider a typical shell Whose circumference c and height h. where, C (3C) = 214 and h(")= y2 Zx (0-2) →x 2 .. ((x) = 2 ITN y h(2) = ZU (2-2)~

Vz (") h (2) ore Now volume of the solid wing shell method is Je cou) a cay S2 (2ru) 7+ (x-2)dx 147)* **(x-2)*** =149152 x(xv 4n+4) de = 1985 J2 (29- 4x² + ant) de [ 94+ amort]: + }(23)-( $ -0+10)] = 146 [15-2? + 2] = 147 (29) [ § -1+?] 14 (24) 16-1$+ 10) (ts) = 14 FT 5 4 - 14 HT ville 2 140 (16) 2 224 0 15 224 IT is