Hello everyone(adsbygoogle = window.adsbygoogle || []).push({});

I have the following question regarding numerical integration twice from acceleration to displacement.

Suppose that a particle has acceleration function of a = t^{t}(which has non-elementary integral), to find the velocity it is easy as I can use Simpson's rule for numerical integration. But now I would like to find the displacement of the particle after some time, let say 5 seconds, how do I calculate it?

Note that I need very accurate answer, so I usually integrate numerically using Excel with thousand interval.

I prefer to use Newton-Cotes formula if possible.

EDIT

I tried using integration by parts, but I always reach a point where I can't continue.

a = t^{t}

Let v = ∫ t^{t}

s = ∫ v

= t*v - ∫ t*t^{t}

= t ∫ t^{t}- ∫ t*t^{t}

For example, to find the displacement after t = 5 seconds

∫ t*t^{t}from 0 to 5 is easy to integrate numerically

But the problem is t ∫ t^{t}I don't know how to do it because there is variable outside the integral.

For those who don't know, I am using integration by parts formula for definite integral, it includes find the value of

( t ∫ t^{t}) from 0 to 5

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Numerical Integration twice (acceleration to displacement)

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**