Integrating Kinematics: Solving for Velocity with Calculus

[PhysicsPrac]

Ok here is my question:

Potential energy = mgh
Kinetic energy = 1/2mv^2
mgh = 1/2mv^2, solving for v you get v = sqrt(2gh)

Now I know v is the same as dx/dt so if I substite in dx/dt for v :

dx/dt = sqrt(2gh)

Multiply by dt:
dx = sqrt(2gh) * dt
Integrate:
x = t*sqrt(2gh)

This should be right, but for some reason it doesn't work when I check it with the well known x = x0 + v0t + 1/2at^2 formula, what am I doing wrong?

 

[Office_Shredder]

I'm assuming that h is supposed to be the distance fallen? That would in fact be the same as your variable x then, not a constant

 

[PhysicsPrac]

ooh I see thanks!