find the arc length of 27y^2 = 4(x-2)^3 from ( 2,0) to (11, 6(3)^(1/2))?

by differentiation, i got dy/dx = 6 (27)^(1/2) (x-2)^(1/2)

and forming the integration equation i got,

integrate ( 972x - 1943) and

then finding the area form x=11 to x=2, my answer was 39375.

but the answer is supposed to be 14.

may i know where i gone wrong?

thanks!