While writing a 2D platformer for Android and PC I came across an issue with my physics. My computer, running at 60 fps had a different jump height than my phone, running at 30. Also, the jump height would be different between jumps. I solved this by implementing Euler integration for my physics. Along the way, I also read about velocity Verlet and the fourth order Runge-Kutta method, which also seem to be popular. My question isn't about specific implementation of the 3, I wanted to ask about the three in comparison to integral approximation used in calculus.

Euler integration seems to be a simple left- or right-endpoint rectangular approximation. Velocity Verlet seems to be a midpoint rectangular approximation and last night, while I should have been sleeping, was thinking about RK4 and thought it sounded like a trapezoidal approximation. Is that right?