Question

5) Use the disk/washer method to set up but do not solve the following Find the volume of the solid generated by revolving the region bounded by y=sin(x), y = 1, x = 0, about the line y = 1.

Answer 1

Solution: Given curves are y=sin x.........(1) y=1 and x = 0 If x=0 then from eqn(1): y=sin(0) = 0 yr y=1 G fly) X=sin 1(y) Oy=0 Shells Method(about the line y = 1) Volume, V = 27 jyf(y)dy y=a Here: y = a = 0, y = b =1 f(y)= X = sin(y) V = 27 Jysin?(y)dy y=0 1 V = 2* sin(y). 2 Tyzo V = 211 -sin-(y) = Jy=0 V = 211 -sin-(y) + y=0 1 V = 21 2 y=0 1 V = 21 dy 2 y=0 -sin(y)+" sin“() ++, VI–y? -sin-"(y) – sin"(y)+3vV1–y? •)-(0-0+0] V = 21 2 Hy=0 V = 271 π π +0 4 8 TT V = 27x 8 V= x2 4 [:: 1 = 3.1416] V = - 2.467 cubic units. 4

(6).Solution: Given curves rae y = e*, x =0, x = 1, y = 0 y x=0 x=1 o y=0 Washer Method (about the line x = 1) b Volume, V = 27 xf(x)dx X=a Here: x = a = 0,X = b = 1 and f(x)=e* V = 27 ſxe* dx x=0 V = 27 [e*(x - 1)]}=0 V = 2[e(1-1) – e°(0 - 1)] V = 21 [0+1] [::eº = 1] V=217 [:: A = 3.1416] :: V = 216.283 cubic units.