If y = tan(x) where x E 0, * is rotated about the x-axis, then the area of the surface of revolution is given by 0 , / 2 , I or # / 4 sec4(x ) , tan-'ly) , ( 1412 ) 2 , sec2(x ) , 2 7T 1 + dx tan(x), 1 Ityz , tan ?( x ) or tan-'cy ) , y, z or tan(x ) ( tan -' (y ) ) 2 1, 71/4, 1/2 or 0 or 0, T1/2, 1 or /4 , Sec4(x), tan(x), sec2 (x ), ( 1 + yz) 2 1 + 4 2 2TT 1 + dy tanz(x ) , (tan-'(y ) ) 2 7/ 4, 1, 01 71 / 2 6 or tan-icy ) x , y , tan(x) or tan"' ()