Catastrophically wrong documentation?
tutorial/SymbolicCalculationsWithUnits under Integrate section.
There are 4 examples of "Calculate displacement over a given time.". All 4 examples have the same physical integrand and limits, but differing units on the integration variable. The results of 1st and 2nd example (250m) and the 3rd and 4th (25/6 m) are saying that the integrated displacement depends on the choice of units for the integration variable????? That's dead wrong!!! Or what am I missing (a brain)?
Here is a cut/paste from the docs:
Calculate displacement over a given time.
In[1]:= Integrate[Quantity[5, "Meters"/"Seconds"^2]*t, {t, Quantity[0, "Seconds"],
Quantity[10, "Seconds"]}]
Out[1]= Quantity[250, "Meters"]
In this form, the variable t is explicitly declared to be measured in seconds.
In[2]:= Integrate[Quantity[5, "Meters"/"Seconds"^2]*t, {Quantity[t, "Seconds"],
Quantity[0, "Seconds"], Quantity[10, "Seconds"]}]
Out[2]= Quantity[250, "Meters"]
Here, the variable t is explicitly declared to be measured in minutes, and the endpoints are automatically converted to the correct units.
In[3]:= Integrate[Quantity[5, "Meters"/"Seconds"^2]*t, {Quantity[t, "Minutes"],
Quantity[0, "Seconds"], Quantity[10, "Seconds"]}]
Out[3]= Quantity[25/6, "Meters"]
In[4]:= Integrate[Quantity[5, "Meters"/"Seconds"^2]*t, {Quantity[t, "Minutes"],
Quantity[0, "Minutes"], Quantity[1/6, "Minutes"]}]
Out[4]= Quantity[25/6, "Meters"]
Calculate displacement symbolically.
In[5]:= Integrate[Quantity[a, "Meters"/"Seconds"^2]*t, {t, Quantity[ti, "Seconds"],
Quantity[tf, "Seconds"]}]
Out[5]= Quantity[((a tf^2)/2 - (a ti^2)/2), "Meters"]
