Question

2. Find the surface area of the object obtained s 2 about the y-axis. by rotating y: 478x2,15*

Answer 1

Given Sol and 1 < x <2 y= 4+372 Surface area of revolution about y-aris farads where ds = it + (dy je de Here, y= = 4+ 3x² dy d (4+3x²) da da d da (4) + (1x2] o + 6a i dy - 64 dx si ds = J+(6x7² dx → ds= 1+36212 da :: Surface are a of revolution about y-anis A = 2T À V+3612 da I

det du 1+ 36 x²= u » d (1+36x²) = du 36(2) ada xda= 22 du And as x varies from 1 to 2 u varies from 37 to 145 2 145 és 277% Vi=3672 dx = 21 su 217 sa (z du) 37 145 T Ju du 36 37 145 슬 u 36 37 = PT du 145 IT T 32 145 3+1 u 1/2+1 W 36 기 36 37 37 3/2 । 54 (145 37 374) = 188:4864 sq. units Aug