Multivariable integral approximation

Hello, first allow me to give some background on my problem:

I have an object being launched under propulsive forces and I need to find a way to express distance traveled in terms of time to see if it will be a safe distance away from a launcher before fins are deployed. The test data I have lasts only a total of 0.2 seconds and consists of accelerometer data associated with time steps.

**The Problem:**

Because I only have accelerations and the times at which they were measured I considered doing an integral approximation using either the Midpoint or Trapezoid rules with F(x)=distance. When my answer came out blatantly wrong (D=0.5*a*t^2 and the timesteps are so small that squaring them made the summed distances far too small to be correct) I realized that F(x) is really F(x,y) because both time and acceleration are changing. I have no idea how to do a multivariable integral approximation, any searching that I have done only leads me to research papers that need to be purchased. Any ideas?