Arc Length Problem: Find Length from y=125 to y=216

[antiflag403]

Hey,
I need some help with an arc length question. It is:
Find the length of the curve:
x=3y^(4/3)-(3/32)y^(2/3) from y=125 to y= 216
So i know i need to use Arc Length=sqrt(1+(dx/dy)^2) but i can't seem to get the right answer.
I have the derivative as 4y^(1/3)-(1/16)y^(-1/3). Squaring that i get:
((4y^(1/3)-(1/16)y^(-1/3))^2
Then took the square root of one and the square root of the above to get:
1+4y^(1/3)-(1/16)y^(-1/3). Then I take the integral of this from 125 to 216 and get an answer of 2105.03125, but this isn't right.
Can someone tell me where i went wrong and point me in the right direction.
Thanks

 

[buzzmath]

the square root of x^2 + y^2 doesn't equal the square root of x^2 plus the square root of y^2. The square root of 25 plus 25 equals the square root of 50 which doesn't equal 10 (the square root of 25 + the square root of 25) just an example.