How to Calculate the Arc Length of x^1/2

[andryd9]

So sorry if this has been discussed elsewhere before. I know it may be trivial but for some reason I just can't get it. I simply can't seem to integrate the square root of (1 + 1/4x). This problem has been highlighted for a reason, but I'm missing the point. Any input is much appreciated.

 

[micromass]

Hi andryd9!

What about a substitution

$$u=\sqrt{1+\frac{1}{4x}}$$

 

[micromass]

Alternatively, you might want to calculate the arc length of x². It should have the same value!

 

[andryd9]

Thank you for the help:)