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Homework Help: Arc Length problem

  1. Apr 18, 2006 #1
    ..Or I think this is considered that...

    Here's the problem as written then I'll get to it:
    Find the lenght of the curve y^2=x^3 from the orign to the point where the tangent makes an angle of 45 degrees with the x-axis.

    Okay, by me posting this, I don't want anyone (nor am I looking for someone) to give me the answer. ...that being said, I feel completely comfortable saying I don't have the FIRST clue of how to start this :)

    So if someone could just help give me a kick-start on this, I'll do my best to take it from there!

    Thanks guys.
  2. jcsd
  3. Apr 19, 2006 #2


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    Homework Helper

    OK, first of all, what is the gradient of a line which makes an angle of 45 degrees with the x-axis ? So what is [tex]\frac{dy}{dx}[/tex] at this point ? Find the x-coordinate of the point on the curve where this condition for the tangent is met.

    The arc length s of a curve between x = a and x = b is given by

    [tex]s = \int_a^b{\sqrt{1 + {(\frac{dy}{dx})}^2}dx}[/tex]

    Can you proceed with that ?
    Last edited: Apr 19, 2006
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