Question

I need help to number 4

Answer 1

Arc length  =INT sqrt(1 + (dy/dx )^2  dx)
                  
 dy dx for 3x^(3/2) -1  =  (9/2) x ^(1/2)

so arc length  =  INT (sqrt ( 1 + (9/2 x^(1/2))^2  ) dx   between x =  0 and 1
                      = INT sqrt    (1 + 81x/4 )  ) dx
                     = (1/243) (81x + 4)^(3/2)

between the limits 1 and 0 this is
    (1/243) (81 + 4)^(3/2)  -  (1/243) ( 4) ^3/2
      =   3.19
arc length = 3.19 to nearest hundredth