Why the integral of |x| is not exact? with SymPy

General Usage
1

Dear all,

I have tried SymPy to compute indefinite integral of |x|, this is the code:

using SymPy

# we can also use @vars x y z
x = symbols("x")
integrate(abs(x))

but the result is like this at terminal, different from the textbook solution:
Capture d’écran_2022-11-23_20-04-32

2

Please post code and REPL output as text. And what do include("plot1.jl") and include("plot.jl") have to do with anything?

3

You need to add an assumption, as is implicit in the textbook:

julia> @syms x y::real
(x, y)

julia> integrate(abs(x),x)
⌠       
⎮ │x│ dx
⌡       

julia> integrate(abs(y),y)
⎧  2            
⎪-y             
⎪────  for y ≤ 0
⎪ 2             
⎨               
⎪  2            
⎪ y             
⎪ ──   otherwise
⎩ 2
1 Like
4

Thanks a lot! I do not know in Julia code I have to do that… put another line for y

5

It is testing the code I name it plot.jl, and plot1.jl is for other code. Sorry for the confusion.

6

The point was to show you needed the assumption (::real did that, though you could do it with keywords to symbols).