Length of curve integral

  • #1

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
 

Answers and Replies

  • #2
LCKurtz
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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.
 
  • #3
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
 
  • #4
LCKurtz
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integrate (9x^4/a^2 + 1/2 + a^4/144x^4)^0.5

Re-check your arithmetic for that first term and you should be able to work out that the quantity under the radical is a perfect square.
 

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