# Arc Length problem

1. Apr 18, 2006

### CACain

..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. Apr 19, 2006

### Curious3141

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 $$\frac{dy}{dx}$$ 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

$$s = \int_a^b{\sqrt{1 + {(\frac{dy}{dx})}^2}dx}$$

Can you proceed with that ?

Last edited: Apr 19, 2006