# Length of curve integral

## Homework Statement

Find the length of the curve y = x^3/a^2 + a^2/12x

between a and a/2

## Homework Equations

Length L = integrate (1+ dy/dx)^2)^0.5

## The Attempt at a Solution

I got to

integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5

but I can't simplify it

LCKurtz
Homework Helper
Gold Member

## Homework Statement

Find the length of the curve y = x^3/a^2 + a^2/12x

Is that last term supposed to be ##\frac {a^2}{12x}## or ##\frac{a^2x}{12}##?
between a and a/2

## Homework Equations

Length L = integrate (1+ dy/dx)^2)^0.5

## The Attempt at a Solution

I got to

integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5

but I can't simplify it

Did you leave out the ##1##? It would help if you showed your work.

Is that last term supposed to be ##\frac {a^2}{12x}## or ##\frac{a^2x}{12}##?

Did you leave out the ##1##? It would help if you showed your work.

the last term is a^2 / (12x) x in the denominator.

yeah i left out the 1, that was a typo.

L = intergrate (1+ (dy/dx)^2)^0.5

thanks

LCKurtz