Finding Length of Curve with Y^3/15 + 5/4y

[whatlifeforme]

Homework Statement

find the length of the curve.

Homework Equations

x=y^3/15 + 5/4y on 3<=y<=5

The Attempt at a Solution

(dy/dx)^2 = Y^4/25 - 1/2 + 25/16y^4

integral (3,5) y^2/5 + 5/4y^2

however, i got the wrong answer. the answer is 67/10.

 

[LCKurtz]

Homework Statement

find the length of the curve.

Homework Equations

x=y^3/15 + 5/4y on 3<=y<=5

Is that 5/(4y) or (5/4)y. If you don't use Latex, at least use parentheses.

The Attempt at a Solution

(dy/dx)^2 = Y^4/25 - 1/2 + 25/16y^4

That isn't (dy/dx)^2 although it may be (dx/dy)^2

integral (3,5) y^2/5 + 5/4y^2

however, i got the wrong answer. the answer is 67/10.

That isn't the right formula for arc length. You need$$
\sqrt{1 + \left(\frac {dx}{dy}\right) ^2}\, dy$$in the integrand.

 

[whatlifeforme]

ok so thus far this should be correct.

L = integral (3,5) sqrt(1 + y^4/25 - 1/2 + 25/16y^4)

this could be further simplified to: sqrt (y^2/5 + 5/4y^2)^2 --->

y^3/15 - 5/4y ] (3 to 5)

the answer is : 67/10 which I'm not getting.

 

[whatlifeforme]

edit: solved.