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Hello everyone

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

Suppose that a particle has acceleration function of a = t

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

Let v = ∫ t

s = ∫ v

= t*v - ∫ t*t

= t ∫ t

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

∫ t*t

But the problem is t ∫ t

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

( t ∫ t

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 numericallyBut 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
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