Originally Posted by

**Calcme** Hey,

So I'm a bit confused on how an answer was reached. The question states:

Find a curve through the point (1,1) whose length integral is given by:

$\displaystyle L = \int_1^4 \sqrt{1+\frac{1}{4x}}dx$. From here I try to use point-slope formula, where m = $\displaystyle \frac{1}{2\sqrt{x}}$ (which comes from taking the square root of $\displaystyle \frac{1}{4x}$. Now, I apply the point-slope formula to try and get the equation of the curve, using:

y - y1 = m(x-x1) ==> y - (1) = $\displaystyle \frac{1}{2\sqrt{x}} (x - (1))$

After adding 1 to both sides and distributing the $\displaystyle \frac{1}{2\sqrt{x}}$ to the (x - 1), I end up with something like:

$\displaystyle y = \frac{x+2\sqrt{x}-1}{2\sqrt{x}}$... which isn't anything like the y = $\displaystyle \sqrt{x}$ answer it SHOULD be.

Can someone point out where I went wrong?