Find the exact length of the curve ???? = (ln ????/2) − (????² / 4),  1 ≤ ???? ≤ 2. And find the exact length of the curve and ???? = (????⁴ /8) + (1 /4????² ), 1 ≤ y ≤ 2.

Exact length of the curve

Step-by-step explanation

Find the exact length of the cence ye ( Inx ) -. ( 2 , ), exez . ablution + Now , difluentiate the given function 9 = ( 1mox ) - (x2g , with recspect to "* " 2 dy 1 - 1 = 1 - x - @ du 2 x 4 2 2x For Finding are . length 1 1 1 , we will use the following formalce L = SD JS It ( d* ) 2 ) L - 2 ) = 1 2 2 du 2 x 4 x 2 4 + 2) 2 dx = 1." ( an + 2 ) da 1 102 + ( 212 + 0#1 = Ling + 1 - 2 - Lin2 + 3 In2+ 3 the exact length of the rence y = In 2 +

Find the exact length of the carve .= ( 8) + ( yo2) -15452 ..... Solution + x = ( 4 " ) + (up2 ) , ky = 2 "Now , differentrate the given function with seespelt to y 143 + 1-2) dy B 2 4 4 2 for Finding are length ( 1 ) , we will use the following Formula 1 - SQ V ( 1 + ( $ 2 ) 2 ) dy 1 = Jav ( 1+ 183 - 293 dy " + do - 1 ) dy 14 9 6 8 1 - + 2 2 4 3 dy 14 4 4 J $1 2( 24 8 L = ( 21 9 + 8 4 1 2 ) 2 = 2 - 16 8 8 - 1 - 2+4 = 2 16 16 the exact length of the cance ?