- #1
Pcmath
- 9
- 0
Hello everyone
I have the following question regarding numerical integration twice from acceleration to displacement.
Suppose that a particle has acceleration function of a = tt (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 = tt
Let v = ∫ tt
s = ∫ v
= t*v - ∫ t*tt
= t ∫ tt - ∫ t*tt
For example, to find the displacement after t = 5 seconds
∫ t*tt from 0 to 5 is easy to integrate numerically
But the problem is t ∫ tt 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 ∫ tt ) from 0 to 5
I have the following question regarding numerical integration twice from acceleration to displacement.
Suppose that a particle has acceleration function of a = tt (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 = tt
Let v = ∫ tt
s = ∫ v
= t*v - ∫ t*tt
= t ∫ tt - ∫ t*tt
For example, to find the displacement after t = 5 seconds
∫ t*tt from 0 to 5 is easy to integrate numerically
But the problem is t ∫ tt 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 ∫ tt ) from 0 to 5
Last edited: